Trains A and B are traveling in the same directions on parallel tracks. Train A is traveling at 80 miles per hour and train B is traveling at 90 miles per hour train A passes a station at 9:15 p.m. if train B passes the same station at 9:45 p.m. at what time will train B catch up to train A?
Two ways to do it: a) in your head or b) by algebra
First way. In your head using the "catch-up" rate of 90-80 or 10mph.
In the half hour from 9:15 to 9:45, train A has gone 40 miles from
the station. So train B has to catch up that 40 miles between them
at a catch-up rate of 10 mph, and so that will take B 4 hours to
catch up to A.
Second way: By algebra:
Make this chart.
distance = rate × time
Teain A
Train B
Let t = the time it takes B to catch up to A, which is
what we want to find.
distance = rate × time
Train A
Train B t
Sinse A traveled 1/2 an hour longer than B did,
we fill in A's time as t+1/2
Fill in the two rates:
distance = rate × time
Train A 80 t+1/2
Train B 90 t
Fill in the distances using d=rt
distance = rate × time
Teain A 80(t+1/2) 80 t+1/2
Train B 90t 90 t
Those two distances from the station are equal
when B catches up to A, so set them equal:
80(t+1/2) = 90t
Solve that and get 4 hours.
Edwin
