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. 

Answer 1

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.