Terran’s running rate is 4 miles per hour faster than her walking rate. She can run 21 miles in the same amount of time it takes her to walk 9 miles. What are her walking and running rates in miles per hour? Write and solve a rational equation to answer the question. Let x be Terran’s walking rate.

She walks at 3 miles per hour, and runs at 7 miles per hour.

Step-by-step explanation:

Let's define:

R = running rate

W = walking rate

We know that:

R = W + 4mi/h

and:

"She can run 21 miles in the same amount of time it takes her to walk 9 miles."

Here we can remember the relation:

Distance = time*speed

The above sentence says that, for a given time T, we have:

21mi = T*R

9mi = T*W

Then we have a system of 3 equations:

R = W + 4mi/h

21mi = T*R

9mi = T*W

To solve this, we could start by isolating T in one of the equations, let's do it in the last one:

9mi/W = T

Now we can replace that in the second one to get

21mi = 9mi*(R/W)

In this equation we could isolate R to get:

R = (21mi/9mi)*W = (7/3)*W

Now we can replace that in the first equation:

R = W + 4mi/h

(7/3)*W = W + 4 mi/h

And now we can solve this for W.

(7/3)*W - W = 4mi/h

(4/3)*W = 4mi/h

W = (3/4)*4mi/h = 3mi/h

And we could use also the first equation to find the running rate:

R = W + 4mi/h = 3mi/h + 4mi/h = 7mi/h

Then:

She walks at 3 miles per hour, and runs at 7 miles per hour.

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step-by-step explanation:

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