Question

From Center Station, a train departs every 30 minutes on the Fast Line and a train departs every 50 minutes on the State Line. If two trains depart from Center Station at 8:00 A.M., one on each of the two lines, what is the next time that two trains, one on each line, will depart at the same time?

Answer 1

Explanation:

You need to find the least common multiple (LCM) of 30 and 50.  First, write the prime factorization of each:

30 = 2×3×5

50 = 2×5²

The LCM must contain all the factors of both, so:

LCM = 2×3×5²

LCM = 150

It will take 150 minutes (or 2 hours and 30 minutes) before two trains depart at the same time again.