Question

Lori recently rode her bicycle to visit her friend who lives 12 miles away. On her way there, her average speed was 7 miles per hour faster than on her way home. If Lori spent a total of 1 hour bicycling, find the two rates.

Answer 1

general formula: distance = rate*time. we can solve for time to get time = distance/rate, which we can abbreviate as t = d/r. we'll write two t = d/r equations, one for the trip there and one for the trip back, and use them to solve for r.

Let's call the rate going home r. For the way there, she travelled 7 mph faster so the way there is r + 7.

using t = d/r for the way home: t = d/r.
for the way there: t = d/(r+7)

she spent one hour in total travelling so the sum of these equations must be 1.
d/r + d/(r+7) = 1

Lori and her friend live 12 miles apart so d = 12.

12/r + 12/(r+7) = 1
solve for r