SOLUTION: Zoha jogs 3 miles per hour faster than she walks. She jogs for 2 miles and then walks for 2 miles. If the total time of her outing is one hour, find the rate at which she walks and

Algebra ->  Linear-equations -> SOLUTION: Zoha jogs 3 miles per hour faster than she walks. She jogs for 2 miles and then walks for 2 miles. If the total time of her outing is one hour, find the rate at which she walks and      Log On


   



Question 190997: Zoha jogs 3 miles per hour faster than she walks. She jogs for 2 miles and then walks for 2 miles. If the total time of her outing is one hour, find the rate at which she walks and jogs?
Answer by orca(409) About Me  (Show Source):
You can put this solution on YOUR website!
Let x represent the speed at which she walks, then the speed at which she jogs is x +3.
The time spent on joging is 2%2F%28x%2B2%29
The time spent on walking is 2%2Fx.
The total time spent is 2%2F%28x%2B2%29%2B2%2Fx
We have already been given the total time spent: one hour.
So 2%2F%28x%2B3%29%2B2%2Fx+=+1
Solving for x, we have
2x+%2B+2%28x%2B3%29+=+x%28x%2B3%29 multiply both sides by x(x+3)
2x+%2B+2x+%2B+6+=+x%5E2+%2B+3x
4x+%2B+6+=+x%5E2+%2B+3x
0+=+x%5E2+-x+-6
x%5E2+-x+-6+=+0
%28x-3%29%28x%2B2%29=+0
So
x=3
or
x=-2(reject this negative solution)
So her walking speed is 3 miles/hour, her joging speed is x + 3 = 6 miles/hour.