Question

Two trains arrived at a station at 2:55 P.M., with one arriving on Track A, and the other arriving on Track B. Trains arrive on Track A every 16 minutes, and they arrive on Track B every 18 minutes. At what time will trains next arrive at the same time on both tracks?

A) 4:07 P.M.
B) 5:19 P.M.
C) 6:31 P.M.
D) 7:43 P.M.

Answer 1

B) 5:19 P.M.

Explanation:

Given that two trains arrived at a station at 2:55 P.M., with one arriving on Track A, and the other arriving on Track B. Trains arrive on Track A every 16 minutes, and they arrive on Track B every 18 minutes.

Now we need to find about at what time will trains next arrive at the same time on both tracks.

Then next time trains arrive at the same time on both tracks. can be found by taking least common multiple of 16 and 18 minutes.

Multiples of 16 and 18 are

16 32 48 64 80 96 112 128 144 160

18 36 54 72 90 108 126 144 162 180

Least common multiple of both is 144

Hence both trains will arrive at the same time after 144 minutes

or at (2:55 PM+144 minutes)

= (2 hours 55 min)+(144 min) PM

= (2 hours 55 min)+(2 hours 24 min) PM

= (2 hours 55 min)+(2 hours 24 min) PM

= 5 hours 19 minutes

Hence correct choice is B) 5:19 P.M.