How long it takes to catch a faster jogger

Question

a jogger who can run a 10 minute mile starts a half-mile ahead of a jogger who can run an 8 minute mile. How long will it take the faster jogger to catch the slower jogger?

Answer 1

Let x = time (in minutes )it takes the faster jogger to                      catch up

 

Rate of slow jogger = 1/10 mile per minute

Rate of fast jogger = 1/8 mile per minute

 

Distance = (rate)(time)

 

Distance traveled by slow jogger = 0.5 + (1/10)x 

Distance traveled by fast jogger  = (1/8)x

 

The faster jogger catches up to the slower jogger when

(1/8)x = 0.5 + (1/10)x

 

Multiply the equation by the LCD, 40:

 

5x = 20 + 4x

  x = 20 minutes