9514 1404 393
Answer:
after 32 minutes
Explanation:
They will both cross the start line together after each has completed a number of full laps in the same time that the other has completed an integer number of full laps. That time will be the least common multiple (LCM) of their lap times, 128 seconds and 120 seconds.
The difference of these times (8 seconds) is also a divisor of both times, so that value is the greatest common divisor (GCD) of the two lap times. The LCM can be figured as ...
LCM(120, 128) = 120×128/GCD(120, 128)
LCM = 120×128/8 = 1920 . . . . . seconds
Converting this to minutes, we get ...
(1920 s)/(60 s/min) = 32 min
They will next cross the start line together after 32 minutes.