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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 that of the passenger train, find the average speed of the two trains



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Let the average speed of passenger train be v km/h
then, speed of express train will be (v+10) km/h
we know that, time = distance/speed
400/v - 400/(v+10) = 2
⇒400(10) = 2(v(v+10))
⇒v² +10v -2000 =0
⇒v² +50v -40v -2000 =0
⇒v(v+50) -40(v +50) =0 
⇒(v+50)(v -40) = 0
⇒ v= 40 or -50
taking positive value,
average speed of passenger train will be 40 km/h
and the average speed of express train will be 50 km/h

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