# Algebra

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Is there an easier way to do this? "A freight train leaves a station at 4:00 p.m. traveling at 30 kilometers per hour. A passenger train leaves 1 hour later, traveling at 50 kilometers per hour. At what time will the passenger train overtake the freight train?

• Algebra -

An easier way than what?

In these kind of problems you have to find which of the three variables, either time, distance or rate, are equal.

In this case, at the moment the 2nd train catches up to the first, they will have gone the same distance.

let the time taken for the 2nd train to catch the first be t hours
so distance covered by the slower train = 30(t+1)
distance covered by the faster train = 50t

50t = 30(t+1)
20t = 30
t = 3/2 hours or 1.5 hours

the faster train left at 5:00 and took 1.5 hours, so it will catch the slower at 6:30 pm

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