Two trains leave a town at the same time heading in opposite directions. One train is traveling 12 mph faster than the other.
After two hours, they are 232 miles apart. What is the average speed of each train?

Answers

Answer 1

Answer:

Step-by-step explanation:

I'm going to paint you a picture in words of what this looks like on paper.  We have a train leaving from a point on your paper heading straight west.  We have another train leaving from the same point on your paper heading straight east.  This is the "opposite directions" that your problem gives you.  

Now let's make a table:

                distance       =        rate      *       time

Train 1

Train 2

We will fill in this table from the info in the problem then refer back to our drawing.  It says that one train is traveling 12 mph faster than the other train.  We don't know how fast "the other train" is going, so let's call that rate r.  If the first train is travelin 12 mph faster, that rate is r + 12.  Let's put that into the table

              distance        =        rate        *        time

Train 1                                        r

Train 2                                    (r + 12)

Then it says "after 2 hours", so the time for both trains is 2 hours:

           

              distance        =        rate        *        time

Train 1                                        r           *          2

Train 2                                  (r + 12)       *          2

Since distance = rate * time, the distance (or length of the arrow pointing straight west) for Train 1 is 2r.  The distance (or length of the arrow pointing straight east) for Train 2 is 2(r + 12) which is 2r + 24.  The distance between them (which is also the length of the whole entire arrow) is 232.  Thus:

2r + 2r + 24 = 232 and

4r = 208 so

r = 52

This means that Train 1 is traveling 52 mph and Train 2 is traveling 12 miles per hour faster than that at 64 mph


Related Questions

A circle has 9 times the area of another circle. If the radius of the larger circle is 27 meters, find the radius of the smaller circle.

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Answer:

Step-by-step explanation:

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-6-(11)
1-17
-5
O 5
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Answer:

-17

Step-by-step explanation:

Hey!!!!

Here's your answer:

-6-(11)

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Two people swing a jump rope. The highest point in the middle of the jump rope is 76 inches above the ground, and the lowest point is 4 inches. The rope makes 4 revolutions per second. Write a model for the height of the rope in inches as a function of time in seconds given that the rope starts at its lowest point.

Answers

Answer:

h(t) = 36sin(1440x)+ 40

Step-by-step explanation:

Given the information:

highest point: 76 inches=>lowest point: 4 inches => 4 revolutions per second => period: [tex]\frac{1}{4}[/tex] per second = [tex]\frac{360}{\frac{1}{4} } =1440[/tex]

y = a sin (bx+c) + k for different values of a, b, and c

=> Amplitude (a) = (highest point - lowest point) / 2 = 36

=> asymptom (k) =  (highest point - lowest point) / 2 = 40

=> model for the height of the rope in inches as a function of time in seconds given that the rope starts at its lowest point is:

h(t) = 36sin(1440x)+ 40

Hope it will find you well.

Answer:

See image below

Step-by-step explanation:

If the area of triangle ABD is 12 square units, what is the area of Rectangle ABCD?

Answers

24 because if you put two triangles together they make a Rectangle

What is the value of x?

Answers

Answer:

D. 75

Step-by-step explanation:

A triangle’s angles equal 180 degrees according to the Triangle Sum Theroem. So, 180-70-35=75.

PLZ MARK BRAINLIEST!!!

Answer:

D. 75 degrees

Step-by-step explanation:

The three angles of a triangle have to add up to be 180 degrees. 70+35= 105, and 180-105= 75. Therefore, the third angle must be 75 degrees in order for it to be a proper triangle.

The cost of a New York Yankee baseball cop is $24,00. The local sporting goods store
mark op rate is 25%. What does the store charge for the baseball cap?

Answers

Answer:

$30

Step-by-step explanation:

30,00                               this is extrz words bc brainly doesnt work well                                              

Pam bought 6.5 pounds of apples for $16.19. If the equation 6.5x = 16.19
models the situation, what does the variable stand for?

Answers

How many apples are in there

Set up an equation to solve for y

Answers

Answer:

The red answer choice

Step-by-step explanation:

Since the sine of an angle is the length of the opposite side divided by the length of the hypotenuse:

[tex]\sin 43=\dfrac{y}{25}[/tex]

Therefore, the correct answer is red. Hope this helps!

Answer:

sin 43 = y / 25

Step-by-step explanation:

sin theta = opposite / hypotenuse

sin 43 = y / 25

Multiply each side by 25

25 sin 43 = y

pls answer this question 43 points

Answers

Answer:

y = -3

Step-by-step explanation:

-3(y-5) = 24

Divide each side by -3

-3(y-5)/-3 = 24/-3

y - 5 = -8

Add 5 to each side

y-5+5 = -8+5

y = -3

Answer:

y= -3

Step-by-step explanation:

-3(y-5)= 24

Do distributive property so, -3y + 15= 24

Subtract 15 from both sides so, -3y + 15 - 15= 24 - 15

Divide -3 from both sides to leave y on one side so, -3/-3y= 9/-3

The answer would be y= -3.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

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Answers

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Look at the attached picture

Hope it will help you

Good luck on your assignment

What is the volume of the cylinder below?
15
12
A. 2160 units 3
B. 56072 units3
C. 1080 units 3
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Answers

hello,

here is your answer:

**********

volume of cylinder = [tex]\pi[/tex]r²h

radius = 12 units

height = 15 units

volume = r² × h × [tex]\pi[/tex]

= 12² × 15 × [tex]\pi[/tex]

= 144 × 15 × [tex]\pi[/tex]

= 2160 × [tex]\pi[/tex]

ans = A. 2160[tex]\pi[/tex] units³

**********

hope this helped,

:)

The volume of cylinder is 2160 [tex]units^{3}[/tex].

What is volume?

Volume is the measure of the capacity that an object holds.

What is the formula for the volume of cylinder?

The formula for the volume of cylinder is

[tex]v = \pi r^{2}h[/tex]

Where,

V is the volume of cylinder.

r is the radius of cylinder.

h is the height of cylinder.

π = 3.14

According to the given question

Height of the cylinder, h = 15 units

Radius of the cylinder, r = 12 units

Therefore, the volume of the cylinder is given by

[tex]v = \pi (12)^{2}(15)[/tex]

v = π × 144 × 15

V = 2160π [tex]units^{3}[/tex]

Hence, the volume of cylinder is 2160 [tex]units^{3}[/tex].

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Answers

Answer:

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Step-by-step explanation:

(6) *3 - (38)

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-20

Answer:

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Step-by-step explanation:

(4 + 2) • 3 – (6² + 2)

6* 3- 38

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Answers

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Step-by-step explanation:

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Answers

Answer:

f(-2) = 1.

Step-by-step explanation:

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f(-2) = 1.

Evaluate f(x) = x + 3 for f(-2)

Given: x = -2

Plug in -2 for x in the equation:

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~

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Answers

Answer:

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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brainliest appreciated

good luck! have a nice day!

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Step-by-step explanation:

Answer:

14/18 and 35/45

Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

The missing options are

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y = e^x - 4

Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Answers

Answer:

1.63

Step-by-step explanation:

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Answers

Answer:

75%

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Select the correct answer from each drop-down menu.
Which system of equations is represented by this graph?

Answers

Answer: y= 5/3x+3

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Step-by-step explanation:

If you drop the menu I could see the choices

Answer:

y = 2x+3

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Step-by-step explanation:

Hope this helps

Find the length of
YZ XY = 8 and XZ = 21.

A.
13
B.
18
C.
21
D.
29



Please select the best answer from the choices provided


A
B
C
D

Answers

Answer:

A. 13

Step-by-step explanation:

YZ + XY = XZ

YZ = XZ - XY = 21 - 8 = 13 units

Jessie rode his bike for 13 hours last month. He rode 7 hours the first week of
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weeks. Which equation or inequality best represents the number of hours. h.
Jesse rode per week for the last three? ​

Answers

Answer:

13=7+3h

Step-by-step explanation:

13 is all together, 7 for first week, and the other 3 have the same amount.

so you can say 13= 7 for the first week+ 3 of the same amount of hour which can be written as 3h.

Find the distance between the points (15, -11) and (15, -19).

Answers

Answer: 8

Step-by-step explanation:

Distance formula: square root x2-x1 squared + y2-y1 squared.

15-15=0

0 squared=0

-19- -11= -8

-8 squared=64

Square root 64= 8

Answer:

8 units

Step-by-step explanation:

the easiest way to work out the distance for these two points is to plot them on a linear graph. as they are in line (because they're both inline with 15 on the x-axis), you just have to count the numbers between -11 and -19. in this case there are 8 units between the two points.

I hope this was helpful :-)

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