How do you find the time?

Question

Joel can run around a 1/4-mi track in 66 sec, and 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 1/4th mile?

Answer 1

t is the amount of time each is running

(t / 60) + (t / 66) = 1

66t + 60t = 3960

126t = 3960

t = 31.4 seconds

Answer 2

each runs for 31 3/7 seconds and they'll meet almost each half way around the track, so that their total combined distances sum to 1/4 of a mile

(31 3/7)/60 + (31 3/7)/66 = 1 lap

= 220/420 + 220/462

= about .5238 + .4762 = 1 lap around the 1/4 mile track

if they both ran the track at 60 seconds it would take 30 seconds each to meet

if they both ran the track in 66 seconds it would take 33 seconds to meet

31 1/2 seconds is the average which is close to 31 3/7 seconds

it's slightly less than the average of the two speeds

the 1/4 mile is irrelevant to the problem, except perhaps to make it appear realistic

and most tracks around football fields are exactly 440 yards = 1/4 mile on the inside of the oval

220/7 =about 31.43 seconds when they meet, run into each other and fall flat on their faces