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Question
The distance between Akola and Bhusawal is 168 km. An express train takes 1 hour less than a passenger train to cover the distance. Find the average speed of each train if the average speed of the express train is more by 14 km/hr than the speed of the passenger train.
Solution
The distance between Akola and Bhusawal is 168 km.
Suppose, average speed of passenger train is x km/hr.
∴ the average speed of express train is (x + 14) km/hr.
∴ the time required for passenger train = `168/x` hours
and the time required for express train = `168/(x+14)` hours
∴ from the given condition,
`168/x-168/x+14=1`
∴` (168x+168xx14-168x)/(x(x+14))=1`
∴` x^2+14x=168xx14`
∴` x^2+14x-2352=0`
∴`x(x+56)-42(x+56)=0`
∴`x(x+56)-42(x-42)=0`
∴` x+56=0 or x-42=0`
∴` x=-56 or x=42`
But speed is not negative
`x=42`
∴ average speed of passenger train =42 km/hr
and average speed of express train =(42+14)=56 km/hr.
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