Question

Elliot and William go running. Elliot ran for 8 miles, and William ran for 12 miles. Elliot finished his run in 40 fewer minutes than WIlliam. If they run at the same speed, for how long did William run?

Answer 1

William ran for 2 hours.

What is the distance of an object?

The distance of an object is the amount of speed covered with respect to time.

Mathematically:

$\mathbf{speed = \dfrac{distance}{time}}$

From the given information:

Elliot ran for 8 miles in x speed, the time at which he ran can be computed as:

$\mathbf{= \dfrac{8}{x}}$ hours

William ran for 12 miles in x speed, the time at which he ran can be computed as:

$\mathbf{= \dfrac{12}{x}}$ hours

If Elliot finished his race 40 minutes fewer than William, then we have:

$\mathbf{=\dfrac{40}{60} \ hour= \dfrac{2}{3 } hour}$

Therefore, the distance at which William ran for can be computed by using the relation:

$\mathbf{\dfrac{8}{x}+\dfrac{2}{3}= \dfrac{12}{x}}$

$\mathbf{\dfrac{2}{3}= \dfrac{12}{x}- \dfrac{8}{x}}$

By solving for x,

$\mathbf{\dfrac{2}{3}= \dfrac{4}{x}}$

By cross multiply;

2x = 12

x = 12/2

x = 6 miles per hour

Thus, William ran for:

= 12 miles/ 6 miles per hour

= 2 hours

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