Train A and B are traveling in the same direction on parallel tracks. Train A is traveling 100 miles per hour and train B is traveling at 120 miles per hour. Train A passes the staion at 7:10 Am. If train B passes the same station at 7:22 Am. At what time will train B catch up with train A?
Here's how to do it in your head. Then we'll do it by algebra.
In your head:
The faster train gains on the slower train by 20mph since 120 is 20mph faster
than 100mph. In the 12 minutes or hr. between 7:10AM and 7:22AM, the
slower train has gotten or 20 miles miles ahead of the faster
train. Since the faster train gains on the slower train by 20mph, the faster
train will catch the slower train 1 hour after it passes the station, or at
8:22AM.
By algebra:
Let x be the amount of time after passing the station that each train has
traveled since passing station at the moment when the faster train catches the
slower train.
Make this chart:
DISTANCE RATE TIME SINCE PASSING STATION
Slower train
Faster train
Put in x for the TIME SINCE PASSING STATION for the Faster train
and their rates as 100mph and 120mph respectively:
DISTANCE RATE TIME SINCE PASSING STATION
Slower train 100
Faster train 120 x
There is 12 minutes between 7:10AM and 7:22AM, so the slower train's time
since passing the station is or hr. more than the faster
train's time since passing the station, so we put x + 1/5 for the slower
train's time since passing the station.
DISTANCE RATE TIME SINCE PASSING STATION
Slower train 100 x + 1/5
Faster train 120 x
Next we fill in the Diustance using Distance = Rate x Time:
DISTANCE RATE TIME SINCE PASSING STATION
Slower train 100(x + 1/5) 100 x + 1/5
Faster train 120x 120 x
The trains will have traveled for the same distance from the station when the
faster train catches up, so we form the equation by setting the two distances
equal:
So the answer is 1 hour after the faster train has passed the station, or 8:22.
Edwin