Question

A train travels 360 km at a uniform speed. If the speed had been 5 km / hr more, it would have taken 1 hour less for the same journey. Find the speed of the train.

Answer 1

To find: Speed of the train 

Method 1: Let the speed of the train be x km/hr.

Time taken to cover 360 km \(=\frac{360}{x}\) hr,

As

Now, given that if the speed would be 5 km/hr more, the same distance would be covered in 1 hour less, i.e.if speed = x + 5, and

then, using distance = speed x time, we have

Now we can form the quadratic equation from this equation

Now, cross multiplying we get 

360 x - x² + 1800 - 5 x = 360 x 

x² + 5 x – 1800 = 0 

Now we have to factorize in such a way that the product of the two numbers is 1800 and the difference is 5x² + 45 x – 40 x – 1800 = 0 

x(x + 45) – 40(x + 45) = 0 

(x + 45)(x – 40 ) = 0 

x = - 45, 40 

since, the speed of train can’t be negative,so, speed will be 40 km/hour.