# Algebra

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Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 40 miles per hour and train B is traveling at 60 miles per hour. Train A passes a station at 5:25 A.M. If train B passes the same station at 5:37 A.M, at what time will train B catch up to train A?

• Algebra -

When train B passes, train A is ahead by 40 miles/hr x (0.2 hr) = 8 miles.

Therafter, the distance between the trains decreases at a rate (60 - 40) = 20 mph. The gap disappears after 8/20 h = 24 minutes.

24 minutes after 5:37 is 6:01 AM

You can also do this with equations, but my way is quicker.

• Algebra -

A travels 12 minutes or 12/60 = 1/5 hour longer that B
If A travels t hours, B travels (t-1/5) hours
They go the same distance (rate*time)
so
40 t = 60(t-1/5)
get t
change it to minutes by multiplying by 60
add it to when A passed the station.

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