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

To find: Speed of the train
Let the speed of the train be x km/hr.

Time taken to cover 360 km = 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 5
⇒ x2 + 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.

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