Question

Train a is traveling @ 60 miles per hour. Train b is traveling @ 80 miles per hour. A arrives @ 9:25 am and b arrives @ 9:40 am what ime will train b catch up to train a?

Answer 1

Do you not mean departs, not arrives? If so:
a travels 40-25 = 15 minutes longer than b

if b travels for t minutes, then a travels for t+15 minutes
a speed = 60/60 = 1 miles/min
b speed = 80/60 = 4/3 miles/min
distances are the same so
1(t+15) = (4/3) t
3 t + 45 = 4 t
t = 45 minutes
so time = 9:40 + 45 = 10:25 am

Answer 2

9:40am - 9:25am = 15min.

15min/60min/h = 0.25h.

When train "B" catches up,the distance
traveled will be the same for each train:

d1 = d2.
60(t+0.25) = 80t,
60t + 15 = 80t,
t = 0.75h = 45min = Time required for
"B" to catch-up.
Time = 9:40 + 45 = 10:25am.