Joel can run around a 1/4 mi track in 66 sec. Jason can run around the track in 60 sec.If the runners start at the same point on the track and run in opposite directions, how long will it take the runners to cover 1/4 mile?

Answer 1

let the time it took be t seconds
they ran the same time

speed of faster runner = .25/60 mi/s =1/240 mi/s
speed of slower runner = .25/66 mi/s = 1/264 mi/s

(1/240)t + (1/264)t = 1/4
(7/880)t = 1/4
t = (1/4)(880/7) = 220/7 seconds
or appr 31.43 seconds

Answer 2

or, consider this a normal work problem:

1/60 + 1/66 = 1/t
t = 220/7