An express train travel from A to B for 4 hours. A normal train travel from B to A for 10 hours. Both of them started at the same time. The average speed of the express train is greater than the average speed of the normal train 90km/h. Find the average speed of the normal train?

Answers

Answer 1

Answer:

The speed of the normal train is 60 kilometers per hour.

Step-by-step explanation:

Let suppose that both trains move at constant speed and cover the same distance. Then, we have the following identity:

[tex]v_{1}\cdot t_{1} = v_{2}\cdot t_{2}[/tex] (1)

Where:

[tex]v_{1}, v_{2}[/tex] - Average speeds of the express train and the normal train, in kilometers per hour.

[tex]t_{1}, t_{2}[/tex] - Travel times of the express train and the normal train, in hours.

In addition, there is the following relationship between average speeds:

[tex]v_{1} = v_{2} + 90[/tex] (2)

By (2) in (1), we have the following expression for the average speed of the normal train:

[tex](v_{2} + 90) \cdot t_{1} = v_{2}\cdot t_{2}[/tex]

[tex]90\cdot t_{1} = v_{2} \cdot (t_{2} - t_{1})[/tex]

[tex]v_{2} = \frac{90\cdot t_{1}}{t_{2}-t_{1}}[/tex]

If we know that [tex]t_{1} = 4\,h[/tex] and [tex]t_{2} = 10\,h[/tex], then the average speed of the normal train is:

[tex]v_{2} = 90\cdot \left(\frac{4\,h}{10\,h - 4\,h} \right)[/tex]

[tex]v_{2} = 60\,\frac{km}{h}[/tex]

The speed of the normal train is 60 kilometers per hour.


Related Questions

deepak wrote out the steps to his solution of the equation 5/2-3x-5+4x=-7/4

Answers

Answer:

x = 3/4

Step-by-step explanation:

5/2-3x-5+4x=-7/4

Combine  like terms

-10/2 + 5/2 +x = -7/4

-5/2+ x = -7/4

Add 5/2 to each side

-5/2+5/2 +x = -7/4 + 5/2

x = -7/4+5/2

Get a common denominator

x = -7/4 + 10/4

x = 3/4

plz anser this nathanmalhotra (if your not them dont anserw) From midnight to 7:00 am, the temperature rose 3/10 °C each hour. If the temperature at midnight was −1°C, what was the temperature at 7:00 am?

Answers

Answer:

11/10°C

Step-by-step explanation:

7 x 3/10 = 21/10

Temperature at midnight = -1°C

Temperature at 7.00 am = 21/10°C -1°C = 11/10°C

Answer:

1.1°C

Step-by-step explanation:

Assuming we are starting at midnight, we know that at midnight it is -1°C. We want to find the temperature at 7:00 AM. Or 7 hours later than midnight. The question says that every hour the temperature rises by 3/10°C. In 7 hours, we need to multiply 3/10*7=21/10=2.1 °C. So, it rises by 2.1 °C. Next add that to the -1 from midnight. Do 2.1+-1=1.1 °C.

Hope this helps!

Intermediate Algebra, Please help

Answers

Answer:

B

Step-by-step explanation:

Other answers look like utter bs

Which is greater than 4?(show work)
(a) 5,

(b) -5,

(c) -1/2,

(d) -25.

Answers

Answer:

Letter A) 5

Step-by-step explanation:

all the other answers are negative so they are less than 4.

5 comes after 4 so 5 is greater than 4.

Hope this is helpful

Find the following probabilities based on the standard normal variable Z. (You may find it useful to reference the z table
answers to 4 decimal places.)
a. P(Z > 1.12)
b. P(Z S-2.35)
c. POSZ s 1.34)
d. P(-0.8 sz s 2.44)

Answers

Answer:

Step-by-step explanation:

a. P(Z > 1.12) = 1-N(1.12) = 1-0.8686431=0.1313569

b. P(Z S-2.35)  => P(Z <= 2.35) = 0.009386706

(please check interpretation of question b)

c. POSZ s 1.34) => P(0 <= Z <= 1.34) =  0.9098773 - 0.5 = 0.4098773

(please check interpretation of question c)

d. P(-0.8 sz s 2.44) => P(-0.8 <= 2.44) = 0.9926564 - 0.2118554 = 0.780801

(please check interpretation of question d)

The probabilities of the standard normal variable are 0.1313, 0.009386, 0.4098773, and 0.780801.

What is a z-score?

The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.

The probability of the following standard normal variable will be given by the z-score table.

a. P(z > 1.12) = 1 - P(z = 1.12) = 1 - 0.8686 = 0.1313

b. P(z ≤ -2.35) = P(z < 2.35) = 0.009386

c. P(0 ≤ z ≤ 1.34) = 0.9098773 - 0.5 = 0.4098773

d. P(-0.8 ≤ z s 2.44) = 0.9926564 - 0.2118554 = 0.780801

More about the z-score link is given below.

https://brainly.com/question/13299273

What is the maximum value of the objective function, P, with the given constraints? P=25x+45y 4x+y≤16 x+y≤10 x≥0 y≥0

Answers

Answer:

the maximum is 450 and the minimum is 0.

Step-by-step explanation:

We know that:

P(x, y) = 25*x + 45*y

First, is easy to see that as x and y increase, also does the value of P(x, y)

So we just need to find the largest and smallest possible values of these variables. We also can notice that the variable y is being multiplicated by a larger coefficient than x, so we prioritize larger values of y when we can.

We know that:

4x+y ≤ 16

x + y ≤10

x≥0

y≥0

Let's start with the second inequality, let's solve this for y:

y ≤ 10 - x

and from the first one we get:

y ≤ 16 - 4*x

Just to show that maximizing x does not work, let's do it:

from the second one, knowing that the minimum value of y is y = 0

we have that:

0 ≤ 16 - 4*x

Here the maximum value that y can take is x = 1

0 ≤ 16 - 4*1 = 0

So we can have the combination y = 0 and x = 1, when we maximize x (here we can see that we should not maximize x)

in this case we get:

P(1, 0) = 25*1 + 47*0 = 25

let's write again our inequalities:

y ≤ 10 - x

y ≤ 16 - 4*x

If now we take the minimum value of x, x = 0, we get:

y ≤ 10

y ≤ 16

Because the first one is more restrictive, we know that the maximum value that y can take (when x = 0) is y = 10

in this case we get:

P(0, 10) = 25*0 + 45*10 = 450

As expected, here is the actual maximum for the given restrictions.

For the minimum, we just need to take the two lowest possible values of x and y, which are the two given by the equalities on:

x≥0

y≥0

The smallest values are:

x = 0

y = 0

Replacing that in the equation we get:

P(0, 0) = 25*0 + 47*0 = 0

So the maximum is 450 and the minimum is 0. (with the given restrictions)

pls tell me the correct option

Answers

Answer: I would go with C I hope i am right!!

Step-by-step explanation:

Answer:

b. [tex] \frac{1}{16} [/tex]

Step-by-step explanation:

A = {2, 3}

B = {4, 6}

C = set of all possible fractions where, the numerators are in set A and the denominators are found in Set B

The 4 possible fractions we can get for set C are as follows:

Set C: { [tex] \frac{2}{4} [/tex] , [tex] \frac{2}{6} [/tex] , [tex] \frac{3}{4} [/tex] , [tex] \frac{3}{6} [/tex] }

Multiply all to get the product of all elements in Set C:

[tex] \frac{2}{4}*\frac{2}{6}*\frac{3}{4}*\frac{3}{6} [/tex]

Simplify where necessary

[tex] \frac{1}{2}*\frac{1}{3}*\frac{3}{4}*\frac{1}{2} [/tex]

[tex] \frac{1*1*3*1}{2*3*4*2} [/tex]

[tex] \frac{3}{48} [/tex]

Simply further

[tex] \frac{1}{16} [/tex]

i can't do this question can someone help me

Answers

Answer:

A=-3

Step-by-step explanation:

To begin, a parabola of form a(x-h)² +k opens upward when a is positive. Similarly, when a is negative, the parabola opens downward. Therefore, a must be negative here, as our expression for the parabola is a(x-0)²+0 = ax², with (0,0) being (h,k) and the vertex.

To determine whether a should be -3 or -0.6, we can think about the values on the graph that correspond to these values. A narrower graph would have a steeper slope. A narrower graph would have a large change in y with little change in x. Therefore, as ax² = y is our equation, and when a=-3, y changes more rapidly relative to when a = -0.6, A=-3 is our answer

Triangle NJK is similar to triangle LMK by​

Answers

Answer:

B

Step-by-step explanation:

SAS cuz ML~NJ and K is common angle

Fill in the blanks using < or >. (a) -3 ...... -4 (b) 6 ....... -20 (c) -8 ...... -2 (d) 5 ...... -7

Answers

Fill in the blanks using < or >.

[tex]\sf \bf {\boxed {\mathbb {ANSWER:}}}[/tex]

(a) -3 [tex]\boxed{ > }[/tex] -4

(b) 6 [tex]\boxed{ >}[/tex] -20

(c) -8 [tex]\boxed{ < }[/tex] -2

(d) 5 [tex]\boxed{ > }[/tex] -7

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{☂}}}}}[/tex]

the figure below is a square . Find the length of side x in simplest radical form with a rational denominator.

Answers

Answer:

[tex]\sqrt{14}[/tex]

Step-by-step explanation:

In any square with side length [tex]s[/tex], the diagonal of the square is equal to [tex]s\sqrt{2}[/tex]. Since the side length of this square is [tex]\sqrt{7}[/tex], the diagonal is equal to [tex]\sqrt{7}\cdot \sqrt{2}=\boxed{\sqrt{14}}[/tex].

Alternatively, you can form two 45-45-90 triangles with the diagonal of the square. The diagonal acts as the hypotenuse for the both these triangles, and the legs of both triangles are equal to the side length of the square. To find the length of the diagonal, use the Pythagorean Theorem, which states [tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse of the triangle, and [tex]a[/tex] and [tex]b[/tex] are the two legs of the triangle.

In this question, both legs are equal to [tex]\sqrt{7}[/tex], and we're solving for the diagonal, which is the hypotenuse in this case:

[tex]\sqrt{7}^2+\sqrt{7}^2=c^2,\\c^2=14,\\c=\boxed{\sqrt{14}}[/tex]

Divisibility rules for 2, 5, and 10


Which numbers are divisible by 5?

A)222

B)185

C)847

or none of these

Answers

Answer:

185 is divisible by 5.

Step-by-step explanation:

Anything that ends in a 0 or 5 can be divisible by 5.

Answer:

Hello There!!

Step-by-step explanation:

The answer is B)185 because a number divisible by 5 ends in 0 or 5.

hope this helps,have a great day!!

~Pinky~

Which similarity postulate or theorem can be used to verify that the two
triangles shown below are similar?

A. SAS theorem
B. SSS theorem
C. AA postulate
D. Similarity cannot be determined.

Answers

Answer:

C

Step-by-step explanation:

AA postulate because we are given 2 of the 3 angles of each triangle. They are both the same in each triangle. Also, we can find the 3rd angle in each triangle. Since both triangles have the exact same angles, they are similar.

The given triangles ΔABC and ΔLMN are similar by AA postulate.

What is a triangle?

A triangle is a three sided polygon that consist of three edges and three vertices .

Here two given triangles are ΔABC and ΔLMN. In these two triangles ∠A=∠L=53° and ∠B=∠M= 72°.

Therefore, the two corresponding angles of triangles ΔABC and ΔLMN are equal . So the third angle of ΔABC is also equal to the corresponding angle of ΔLMN.

Hence two triangles are similar by AA postulate.

Thus two triangles are similar by AA postulate. So option (C) is correct.

To learn more about triagles click here:

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Question 17 of 25
Imagine that you are given two linear equations in slope-intercept form. You
notice that both the slopes and the y-intercepts are the same. How many
solutions would you expect for this system of equations?
A. infinitely many
B. cannot be determined
C. O
D. 1

Answers

Answer:

A. infinitely many

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

m - slope b - y-intercept

Solving systems of equations

Step-by-step explanation:

If 2 lines are parallel (same slope, different y-intercept), they would have no solution.

If 2 lines were the same (same slope, same y-intercept), they would have infinite amount of solutions.

What are the measure of ∠1 and ∠ 2 ? Show your work or explain

Answers

Answer:

I need the picture.

which statement about 0 is true ?

Answers

Answer:

❍ C. tan θ = 8 / 15

Step-by-step explanation:

Using trigonometry functions

sin θ = opposite side / hypotenuse

= 8 / 17

tan θ = opposite side / adjacent side

= 8 / 15

Hence, tan θ = 8 / 15 which is option C. is the correct statement.

find the surface area of the composite figure. 6cm 5 cm 20cm 4cm 12cm 6cm​

Answers

Answer:

644 cm²

Step-by-step explanation:

Surface area of the composite figure = surface area of the large rectangular prism + surface area of the small rectangular prism - 2(area of the surface of the small rectangular prism that joins the larger prism)

✔️Surface area of the large rectangular prism = 2(LW + LH + WH)

L = 6 cm

W = 5 cm

H = 20 cm

Surface area = 2(6*5 + 6*20 + 5*20)

= 500 cm²

✔️Surface area of the small rectangular prism = 2(LW + LH + WH)

L = 6 cm

W = 4 cm

H = 12 cm

Surface area = 2(6*4 + 6*12 + 4*12)

= 288 cm²

✔️area of the surface of the small rectangular prism that joins the larger prism = L*W

L = 12 cm

W = 6 cm

Area = 12*6

= 72 cm²

✅Surface area of the composite figure = 500 + 288 - 2(72)

= 644 cm²

Farida bought 20 stamps consisting of 20 sen stamps and 60 sen stamps. The total cost of the stamps is RM8.80. How many 20 sej stamps did Farida buy?

Answers

Answer:

# of 20cent stamps = 8

Step-by-step explanation:

Let the  number 20cent stamps be = x

Let the number 60 cents stamps be = y

Total number of stamps => 20 = x + y ----------- ( 1 )

Total cost of the stamps = 8.80

That is, 0.20x + 0.60y = 8.80 ------------- ( 2 )

      ( 2 ) => 20x + 60y = 880

            => x + 3y = 44

           =>  x = 44 - 3y

Substitute x in  ( 1 ) => x  +  y = 20

                                 44 - 3y + y = 20

                                     - 2y = 20 - 44

                                     - 2y = - 24

                                       2y = 24

                                       y = 12

Substitute y = 12 in  ( 1 ) => x + y = 20

                                         x + 12 = 20

                                            x = 8

Choose the best graph that represents the linear equation: -2y = x + 6 Graph A On a coordinate plane, a line goes through (negative 6, 0) and (1, negative 3). Graph B On a coordinate plane, a line goes through (0, 3) and (2, 4). Graph C On a coordinate plane, a line goes through (0, 3) and (2, 2). Graph D On a coordinate plane, a line goes through (0, negative 3) and (6, 0). a. Graph A c. Graph C b. Graph B d. Graph D Please select the best answer from the choices provided A B C D

Answers

Answer:

A

Just took the test, you're welcome :)

-2y = x + 6 Graph A On a coordinate plane, a line goes through (negative 6, 0), and (1, negative 3) is the right answer

What is a coordinate plane?

The coordinate plane is a system of representation and description of points and lines. The vertical (y) and horizontal (x) axes form the coordinate plane. The coordinate plane has four quadrants. The point where these lines connect is called the origin (0,0).

The properties of each of the four quadrants of the coordinate plane are:

Quadrant I: Positive x and positive y.Quadrant II: Negative x and positive y.Quadrant III: Negative x and Negative y.Quadrant IV: Positive x and negative y.

Learn more about coordinate plane here:https://brainly.com/question/10737082

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pls tell the answer by step by step

Answers

The point lies in 2nd quadrant.

Answer:

second quadrant

Step-by-step explanation:

here , -2 is x component and y component is 5

since x component is negative and y component is positive it lies on the second quadrant.

Note: if both x and y component are positive then the point lies on first quadrant.

id x component is negative and y component is positive then the point lies on second quadrant.

if x both x and y component are negative then the point lies on third quadrant.

if x component is positive and y component then the point lies on fourth quadrant.

Rachel loaned Adam $8510 at an interest rate of 13 % for 2 years. How much will Adam pay Rachel at the end of 2 years? Round your answer to the nearest cent, if necessary.

Answers

Rachel will owe Adam 10,722.6 at the end of the 2 years.

Solve for x.
3:12 = x:16
64
4
2 1/4

Answers

Hi!

i think We can set up a proportion to solve this

\frac{3}{12} \frac{x}{16}

12

3

16

x

Cross multiply

3 x 16 = 48

48/12 = 4

The answer is 4

Hope this helps! :)

what is the gradient of line Y =-3×+5​

Answers

Gadient: -3
The form: y=ax+b
a: gadient
b: intercept

A fishing trawler sails from port P in the direction 024o for 30 km, and then in the direction 114o for 20 km. Calculate: a) the distance and bearing of the trawler from P b) the direction in which the trawler must sail in order to return to P
Please use diagrams to explain.

Answers

Answer:

write these time in words 3:45

find the volume of the following solid figures. show your solution​

Answers

Answer:

37.68m^3

2143.57 m^3

Step-by-step explanation:

Volume of a cone 1/3(nr^2h)

n = 3.14

(1/3) x (3^2) x 4 x 3.14 = 37.68

Volume of a sphere = 4/3 x pi x r^3

4/3 x 8^3 x 3.14 =

Can someone pls help me!

Answers

Answer: y =2x-5

Work:

2x-y=5

-y=-2x+5

-1y/-1 = -2x+5/-1

y =2x-5

Which description matches the expression 13 minus StartFraction 5 Over y EndFraction? the difference of thirteen and the product of five and a number the quotient of five and a number minus thirteen the difference of thirteen and the quotient of five and a number the sum of thirteen and the quotient of five and a number

Answers

Given:

The expression is:

[tex]13-\dfrac{5}{y}[/tex]

To find:

The description that matches the given expression.

Solution:

We have,

[tex]13-\dfrac{5}{y}[/tex]

Here, [tex]\dfrac{5}{y}[/tex] is describes as the quotient of five and a number and the minus sign describes the difference between 13 and the quotient.

So, the description that matches the given expression is "difference of thirteen and the quotient of five and a number".

Therefore, the correct option is C.

Answer:

the difference of thirteen and the quotient of five and a number

Step-by-step explanation:

The capacity of a CD-ROM is 800 MB (800 x 20 raised to 20 bytes). It stores information along a spiral track. If each byte uses a space of 9 microns, what is the length of the complete track in m? (Hint: 1 micron= 10 Raised to-6m)

Answers

Answer:

The length of the complete track= [tex]7.549\times 10^{23} m[/tex]

Step-by-step explanation:

We are given that

Capacity of CD-ROM=800MB=[tex]800\times 20^{20} bytes[/tex]

1 byte=9 microns

[tex]1micron=10^{-6}m[/tex]

We have to find the  length of the complete track in m.

We change MB into  micron

[tex]800\times 20^{20} bytes=800\times 20^{20}\times 9microns[/tex]

=[tex]7200\times 20^{20} microns[/tex]

Now, we change micron into m

[tex]7200\times 20^{20} microns=7200\times 10^{-6}\times 20^{20} m[/tex]

=[tex]7.549\times 10^{23} m[/tex]

Hence, the length of the complete track= [tex]7.549\times 10^{23} m[/tex]

Can someone help me out with this

Answers

Answer:

Step-by-step explanation:

a) 7² + a⁰ = 7*7 + 1 = 49 + 1 = 50

Anything raised to 0 is 1  {Eg: 15⁰ = 1 ,(-k)⁰ = 1}

b) 4³ - 3¹ = 4*4*4 - 3 = 64 - 3 = 61

c) 12x⁶ * 7x⁸ = (12*7)*x⁶⁺⁸ = 84x¹⁴

In exponent multiplication, If x is a rational number and a & b are two integers, then xᵃ * xᵇ = xᵃ⁺ᵇ

d) 49a¹³ ÷ 7a⁸ = (49 ÷ 7) * a¹³⁻⁸ = 7a⁵

In exponent division, If x is a rational number and a & b are two integers, then xᵃ ÷ xᵇ = xᵃ⁻ᵇ

e) (2y³)⁵ = 2⁵*(y³)⁵ = 32y³ˣ⁵ = 32y¹⁵

question is worth 4 marks The ble below show the food the number of calories per serving and the number of servis hained Open strict diet where he can only have a total of 1800 calories per day notion in the table have create a balanced meal of 3 items, one serving each he bave for Number of Se 15 2​

Answers

Answer:

തത് httht bytbtybbybbtybbybyybyv6vyvyvtv5ct

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