Chapter 2.7, Problem 6STP

Elisabeth goes on a 5 mile run each Saturday. Her run typically takes her 45 minutes. She wants to increase this distance to 7 miles. Determine the proportion you use to find the time it would take her to run 7 miles. Solve the proportion. What proportion can be used to determine the time it takes for her to run a marathon, which is approximately 26 miles? What is her time?

To determine

To find: We are asked to find the proportional equation to find time that would take her to run 7 miles. And solve it. Then find proportional equation to the time to run for 26 miles and the time.

Answer to Problem 6STP

Proportional equation to find 7 miles run is $\frac{x}{45}=\frac{7}{5}$

  $X=63$ minutes or 1 hour 3 minutes

Proportional equation to run 26 miles is $\frac{45}{5}=\frac{y}{26}$

Her time to run on Marathon is 234 minutes or 3 hours 54 minutes.

Explanation of Solution

Given information: Elisabeth goes 5 miles in 45 minutes. She wants to increase this distance to 7 miles.

Calculation:

Let she take ‘ x’ minutes to run for 7 miles.

And it takes 45 minutes to run for 5 miles.

So, we can set up proportional equation as $\frac{x}{45}=\frac{7}{5}$

Cross multiply, $5x=315$

Divide both sides by 5.

X= 63minutes

We know 60 minutes is 1 hour.So, 63 minutes is 1 hour 3 minutes.

Now, let’s set up proportional equation to run for 26 miles. Let he takes ‘ y’ minutes

The proportional equation is $\frac{45}{5}=\frac{y}{26}$

We can solve it for y . Cross multiply, we get $1170=5y$

Divide both sides by 5

  $Y=234$ minutes.

Let’s change it to hours. We know 1 hour =60 minutes

So, 234 minutes = $\frac{234}{60}$ = 3 hours 54 minutes.