Saved Bookmarks
| 1. |
27. A goods train leaves a station at p, followed by an express train, which leaves at 8pmand travels 20 km/h faster than the goods train. The express train arrives at a station, 1040km away, 36 min before the goods train. Assuming that the speeds of both the trains remainconstant between the two stations, calculate their speeds |
|
Answer» 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 |
|