+1836 Running at constant speed, Andy can run around a circular track once in 40 seconds. Bob, running in the opposite direction, slaps hands with Andy every time they run past each other. If they only slap hands every 15 seconds, how many seconds does it take Bob to run around the track once?
+129852 Let the distance around the track = d
Then, every second, Andy runs d/40th of a lap.
Let them start at the same place running in opposite directions.
So, in 15 seconds, Andy runs (d/40)(15) = (15/40)d = (3/8)d
And since they meet, Bob must run d - (3/8)d = (5/8)d every 15 seconds........so........
15/ [(5/8)d] = x / [1 d] where x is the total number of seconds it takes Bob to complete 1 lap......
cross-multiply.....
15d = x(5/8)d
15 = (5/8)x
(15)(8/5) = x = 24 seconds = Bob's time to run one lap.....
