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Guru

A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And, if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train. Q.3

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How i solve this optional chapter question, of exercise 3.7 in easiest way . I think it is also an important type of question. A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And, if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.

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1. Let the speed of the train beÂ xÂ km/h and the time has taken beÂ yÂ h. The total distance is thenÂ xyÂ km. Case1: Speed increases byÂ 10Â km/h and the time taken reduces byÂ 2Â hours.

The distance traveled remainsÂ xyÂ km.
(x+10)(yâˆ’2)=xy
Therefore,Â xyâˆ’2x+10yâˆ’20=xy
â‡’âˆ’2x+10yâˆ’20=0
â‡’âˆ’2x+10y=20Â ———- (1)
Case 2:
Speed decreases byÂ 10Â km/h, then the time taken increases byÂ 3Â hours.
However, the distance remains,xyÂ km.
(xâˆ’10)(y+3)=xy
Therefore,Â xy+3xâˆ’10yâˆ’30=xy
â‡’3xâˆ’10yâˆ’30=0
â‡’3xâˆ’10y=30Â ———- (2)
â‡’x=50Â km/h
Using this in (2), we get
150âˆ’10y=30
â‡’y=12
Therefore, the distance isÂ 50Ã—12=600Â km

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