How far has Jim run when he is caught?

Question

Jim and Derry start at the same time and place, running a 1.5 mile loop. Jim runs at 8.5 minutes per mile. Derry runs at 7 minutes per mile. Derry eventually catches Jim.

Answer 1

Some correct assumptions:

Jim and Derry start the race at the same time and meet at the same time.

The time that they each are running is equal.

 

Derry doesn't acutually "catch" Jim. Derry is always ahead of Jim since he is running faster. On a loop Derry shall complete a lap and then approaches Jim from "behind." This is called "lapping."

Derry runs one lap, 1.5 miles, more than Jim runs.

 

For Jim:

d = (1/8.5)t

d/(1/8.5) = t

8.5d = t

 

For Derry

d +1.5 = (1/7)t

(d + 1.5)/(1/7) = t

7(d + 1.5) = t

7d + 10.5 = t

 

Equating the two

8.5d = 7d + 10.5

1.5d = 10.5

d = 7

 

check

 

7(1/8.5) = 8.5(1/7)

8.5(7) = 7(8.5)

59.5 = 59.5

 

Jim runs 7 miles.