Two athletes practice for a marathon by running back and forth on a 11-mile course. They start running simultaneously, one at a speed 2 miles faster than the other. How fast does each run if they meet 1 hr 6 minutes after starting? (The faster one is already returning at this point.) How far from the starting point do the runners meet?

Answers

Answer 1

Answer:

Faster runner speed: 11 mph

Slower runner speed: 9 mph

Distance from starting point: 9.9 miles

Step-by-step explanation:

Let the slower runner speed be: x

Faster runner speed: x+2

1 hour 6 minutes = 1.1 hours

Slower: 1.1(x) = 1.1x miles

Faster: 1.1(x+2) = 1.1x+2.2 miles

This means that the faster runner had gone 2.2 miles more than the slower runner.

1.1x + 2.2 > 11 miles (This is true as we know the faster runner is coming back from the 11 mile run)

1.1x > 11 - 2.2 miles

1.1x > 8.8 miles

x > 8.8 / 2.2 miles

x > 8 mph

1.1x < 11 miles (we know this is true as the slower runner has to have gone less than 11 miles as the faster runner met him on his way back)

x < 11 / 1.1 miles

x < 10 miles

8 < x < 10

Although x could be any number including decimal between 8 and 10, the obvious first answer would be 9. However we need to check if this answer is correct.

Slower runner distance to the end:

1.1(9) = 9.9 miles

11 - 9.9 = 1.1 miles

Faster runners distance from the end (when coming back)

1.1(9+2) = 1.1(11) = 12.1 miles

12.1 - 11 = 1.1 miles

The speeds 9 mph and 11 mph are now proven to be the right speeds. Using our equation before, we can figure out the distance from the starting point that they meet at. This is just how far the slower runner has gotten. So, 1.1(9) = 9.9 miles from the starting point

Answer 2

The runners meet at a distance of 8.8 miles from the starting point.

How to determine the time required for two runners to meet each other

According to statement, each runner must run back and forth on a 11-mile course. After supposing that each runner moves at constant speed, expressions for each runner are presented below:

Fast runner reaches the end

[tex](v+2)\cdot 1.1 = 11[/tex] (1)

Fast runner comes back from the end

[tex]x = \left(v+2\right)\cdot (1.1-t)-(v+2)\cdot t[/tex] (2)

Slow runner meets fast runner

[tex]x = v\cdot 1.1[/tex] (3)

Where:

[tex]v[/tex] - Speed of the slow runner, in miles per hour.[tex]t[/tex] - Comeback time of fast runner, in hours.[tex]x[/tex] - Point of the track where runners meet each other, in miles.

By (1), we obtain the speed of the slow runner:

[tex]v = \frac{11}{1.1}-2[/tex]

[tex]v = 8\,\frac{mi}{h}[/tex]

The position from the starting point is calculated by (3):

[tex]x = (8\,mi)\cdot \left(1.1\,h\right)[/tex]

[tex]x = 8.8\,mi[/tex]

The runners meet at a distance of 8.8 miles from the starting point. [tex]\blacksquare[/tex]

To learn more on linear functions, we kindly invite to check this verified question: https://brainly.com/question/17058347


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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

Edge 2021.

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

Let [tex]x[/tex] denotes number of drinks and [tex]y[/tex] denotes number of pastries.

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Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

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Answers

Answer:

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Step-by-step explanation:

The computation of the distance from his walk to the bus stop is given below:

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Answer: The answer is 468.

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

Use Pascal's Triangle to help find the missing values. x^4-4x^b+6x^2-ax+1

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Answers

Answer:

The value of a = 4 , b = 3

Step-by-step explanation:

Given the equation,

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                              1                     2

                   1                   2                        1

         1                   3                   3                         1

 1                4                   6                      4                       1

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Now, as given equation be x⁴ - 4[tex]x^{b}[/tex] + 6x² - ax + 1

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So, we get

a = 4 , b = 3

Please help:

What are the solutions to the system of equations?

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The solution with the larger x value is (?)

Answers

Answer:

(- 1, - 2 ) and (1, 2 )

Step-by-step explanation:

Given the 2 equations

x² + y² = 5 → (1)

y = 2x → (2)

Substitute y = 2x into (1)

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x² = 1 ( take the square root of both sides )

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The solution with the larger x value is (1, 2 )

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It’s 36,000, because the total income in one year is 120,000 and if you subtract the total income from the tax paid per year you get the answer.
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A ball is thrown straight up from the top of 128 foot building with an initial speed of 32 feet per second. How long will it take for the ball the hit the ground? How high will the ball be after 3 seconds?

Answers

The ball drops 32 ft per second
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Which system of inequalities has no solution?

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Answer:

i think c

Step-by-step explanation:

-7x2+1 need help plz

Answers

Answer:

-7 × 2 + 1 =

-13

Step-by-step explanation: I hope it helps.

The point Q(-6, 3) is reflected over the y-axis. What are the coordinates of the resulting
point, Q'?

Answers

Answer:

Q' = (6,3)

Step-by-step explanation:

You can think of this problem in two ways:

Graph:

I've shown my working for this, where I've counted how many units it takes to get from point Q to the axis through which im reflecting. There are 6 units between Q and the y axis, so naturally there should be 6 units between Q' and the y axis.

Coordinates:

Since this is a reflection through an axis, we can assume that the the x coordinate of point Q' will be equal and opposite to Q. Therefore, while the x coordinate of Q was -6, of Q' it's 6

Alfred has 10 more tokens than Clarissa. Clarissa has twice as many tokens as Benji. They have 85 tokens altogether. How many tokens does each person have.

Answers

Answer:

Alfred has 40 tokens

Clarissa has 30 tokens

Benji has 15 tokens

Step-by-step explanation:

Let's give each person a variable:

A for Alfred

C for Clarissa

B for Benji

Now, we can take what the question is saying and convert them into equations:

Alfred has 10 more tokens than Clarissa can look like this:

A = C + 10

Since Alfred has 10 more coins than Clarissa we can take C and add 10 to find how many tokens Alfred has.

Clarissa has twice as many tokens as Benji looks like this:

C = 2B

Since Clarissa has twice as many tokens as Benji we can multiply B (how many tokens Benji has) by 2.

Lastly, they have 85 tokens all together:

A + B + C = 85

We have these 3 equations:

A = C + 10

C = 2B

A + B + C = 85

Now, we can substitute some variables:

A = (2B) + 10    Since C is equal to 2B we can substitute 2B in for C in the first equation.

We have found what A equals, we can plug that in to the last equation:

(2B) + 10 + B + C = 85

We can also substitute the second equation into the third equation:

(2B) + 10 + B + 2B = 85

Combine like terms:

5B + 10 = 85

Solve

5B = 75

B = 15

This means that Benji has 15 tokens. Now we can find how much the other children have:

C = 2(15) = 30

Clarissa has 30 tokens

A = 30 + 10

A = 40

Alfred has 40 tokens.

Answer:

Alfred has 40 tokens

Clarissa has 30 tokens

Benji has 15 tokens

Checking the Answer

A + B + C = 85

40 + 15 + 30 = 85

85 = 85

I hope this helps!!

- Kay :)

It is important for engineers design and building so understanding the relationship between the height and volume of the building. A taller building if not billed correctly is more likely to collapse, because a small increase in height leads to a large increase in volume. an engineer builds to build a models of different sizes in the shape of square blocks . the smaller building has a height of 1m, and volume of 1m^3. The volume of the larger building is 125m^3. The height of the building, represented by X, is equal to the cube root of the buildings volume. The equation below can be used to find X, in meters. X^3=volume determine how much taller, in meters, the height of the larger building is then the smaller building.Mm

Answers

Answer:

Larger building is 4 meters taller than smaller building.

Step-by-step explanation:

Formula to get the height 'x' of a building having volume = x³ is,

x = [tex]\sqrt[3]{\text{Volume of the building}}[/tex]

Height of the smaller building,

[tex]x_1=\sqrt[3]{1}[/tex]

[tex]x_1=1[/tex]

Similarly, height of the larger building = [tex]\sqrt[3]{125}[/tex]

                                                               = [tex]\sqrt[3]{5^3}[/tex]

                                                               = 5 meters

Difference in the heights of the buildings = 5 - 1

                                                                     = 4 meters

Therefore, difference is the height of larger and smaller building is 4 meters.

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