Question

A goods train leaves a statipon at 6 p.m., followed by an express train which leaves at 8 p.m. and travels 20 km/hr faster than the goods train. The express train arrives at a station, 1040 km away, 36 minutes before the goods train. Assuming that the speeds of both the trains remain constant between the two stations, calculate their speeds.

Answer 1

HEY!!!!

Let the speed of the goods train be 'x' km/hrThen, speed of express train=(x+20) km/hrGoods train leaves a station at 6pm and express train leaves the station at 8pmalso express train reaches its destination 36min before goods train.We known that,Time taken = distance covered /speedTotal distance=1040kmTime taken by goods train to cover1040 km=1040/x
Time taken by express train to cover 1040 km=1040/(x+20)As per given condition we have,1040/x=1040/(x+20)+2(36/60)
1040/x-1040/(x+20)=2(3/5)
(1040x+20800-1040x)/(x²+20x)=13/5
13x²+260x=104000
x²+20x-8000=0
x²+100x-80x-8000=0
x(x+100)-80(x+100)=0
(x-80)(x+100)=0
x=80 (or) x=-100Here x>0Therefore x=80
Hence speed of goods train=80 km/hrand speed of express train=100 km/hr.
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