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Question

# An express train takes 2 hour less time than a passenger train to travel 400 km between two stations (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 10 km/h more than of the passenger train, find the average speed of the two trains

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Solution

## Let the speed of express train be x km/hLet the speed of passenger train be y km/hx=y+10..........(i)Time is defined as the ratio of distance to speed.Time of express train is less than passenger train by 2 h400x+2=400y...........(ii)Substituting value of x from (i) in (ii), we get:400y+10+2=400yRearranging terms, we get:y2+10y−2000=0⇒y2+50y−40y−2000=0⇒(y+50)(y−40)=0⇒y=−50ory=40Speed cannot be negative, therefore y=40From equation (i), x=y+10=50Hence, average speed of express train is 50 km/haverage speed of passenger train is 40 km/h

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