Train A leaves a station at 8:00 and travels at 100 km per hour towards the next city. One and a half hours later, Train B, an express, leaves the same station, traveling at 160 km per hour along the same route. At what time will Train B overtake the slower train?

Question

10-07-2015
Mathematics

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Train A leaves a station at 8:00 and travels at 100 km per hour towards the next city. One and a half hours later, Train B, an express, leaves the same station, traveling at 160 km per hour along the same route. At what time will Train B overtake the slower train?

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naǫ naǫ · Answer 1 · 2015-07-11T15:26:16+02:00

Let t be time in hours.

Train A travels at 100 km per hour, so after t hours it will be 100t km from the station.

Train B travels at 160 km per hour, but it leaves the station one and a half hours later than train A, so its time is (t-1.5) hours. After (t-1.5) hours it will be 160(t-1.5) km from the station.

Train B will overtake train A when their distances from the station are equal.
[tex]100t=160(t-1.5) \\ 100t=160t-240 \\ 100t-160t=-240 \\ -60t=-240 \\ t=\frac{-240}{-60} \\ t=4[/tex]

Train B will overtake train A after 4 hours since train A left the station. It left the station at 8:00, so train B will overtake it at 12:00.