Answer: 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.
