riding a bicycle

Question

A man rode a bicycle for 12 miles and then hiked an additional 8 miles. The total time for the trip was 5 hours. If his rate when he was riding a bicycle was 10 miles per hour faster that his rate walking, what was each rate?

Answer 1

Let x = biking speed 

 

Let y = walking speed

 

12/x = biking time

 

8/y = walking time 

 

x = y + 10

 

12/x + 8/y = 5

 

12/(y + 10) + 8/y = 5 

 

Find least common multiple which is y(y + 10). Multiple the whole equation by it.

 

12y + 8y + 80 = 5y^2 + 50y

 

20y + 80 = 5y^2 + 50y

 

5y^2 + 30y - 80 = 0

 

y^2 + 6y - 16 = 0

 

(y + 8)(y - 2) = 0

 

y = -8 

y = 2

 

Use the positive answer only.

 

The walking speed is 2 mph, and the biking speed is 12 mph.