# math/algebra

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Trains A and B are traveling in the same direction on parallel tracks. Train a is traveling at 100 mph and train B is traveling 120 mph. Train a passes a station at 7:20 P.M. If train B passes the same station at 7:35 P., at what time will train B catch up to train A?

• math/algebra -

By 7:35, train A would have gone 15min. past the station. The distance travelled would have been 100 mph*15/60 hours = 25 miles.
Train B catches up at the rate of 120-100 mph=20 mph. How long would it take to catch up?

• math/algebra -

7:35 PM - 7:20 PM = 15 min = 0.25 h,

When train B catches up with A, their
distance traveled will be equal. But A
traveled that distance in 15 min(0.25h)
less. Therefore:

d1 = d2,
100t = 120(t - 0.25),
100t = 120t - 30,
100t - 120t = -30,
-20t = -30,
t = 1.5 h = train A time traveled.
(t - 0.25) = 1.5 - 0.25 = 1.25 h =
1:15 = Time needed for B to catchup,

B caughtup at: 7:35 PM + 1:15 = 8:50PM.

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