algebra helppppppp?!?!?

Question

train a leaves a staition travelling at 30 miles per hour four hours later train b leaves the same direction travelling in the same direction at 40 miles per hour how long did it take for train b to catch up to train a?

Answer 1

it took train b three hours to catch up and more than that to beat train a

Answer 2

think of the formula distance = rate * time

since you are looking for the time when b catches up to a, that is the point where a and b both have gone the same distance.

a leaves the station at 30 mph four hours before b, so when b starts a has already gone 120 miles

so for train a:
d=120 + 30(t)

and for train b:
d=40(t)

if this is confusing, think of it like a has a 120 mile head start.

since they go the same distance,
d=d
120 + 30t = 40t
120 = 10t
12 = t

so after 12 hours, b will catch up to a

Answer 3

12 hours

Answer 4

12 hours

Answer 5

40 mins