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Question
Two trains leave a railway station at the same time. The first train travels due west and the second train due north. The first train travels 5 km/hr faster than the second train. If after 2 hours, they are 50 km apart, find the speed of each train.
Solution
Let take the speed of the second train to be x km/hr
Then, the speed of the first train is (x + 5) km/hr
Let O be the position of the railway station from which the two trains leave.
Distance travelled by the first train in 2 hours
= OA
= Speed × Time
= 2(x + 5) km
Distance travelled by the second train in 2 hours
= OB
= Speed × Time
= 2x km
By Pythagoras Theorem, we have
(AB)2 = (OA)2 + (OB)2
`=>` (50)2 = [2(x + 5)]2 + (2x)2
`=>` 2500 = 4(x + 5)2 = 4x2
`=>` 2500 = 4(x2 + 25 + 10x) + 4x2
`=>` 8x2 + 40x – 2400 = 0
`=>` x2 + 20x – 15x – 300 = 0
`=>` (x + 20)(x – 15) = 0
`=>` x = –20 or x = 15
`=>` x = 15 ...[∵ x cannot be negative]
Hence, the speed of the second train is 15 km/hr and the speed of the first train is 20 km/hr.
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