Question

A train travels a distance of 300 km at a constant speed. If the speed of SE the 20 train is increased by 5 km an hour, the journey would have taken 2 hours less. Find the original speed of the train.

Answer 1

Total distance travelled = 300 km

Let the speed of train = x km/hr

We know that,

Hence, time taken by train = 300/x

According to the question,

Speed of the train is increased by 5km an hour

∴ the new speed of the train = (x + 5)km/hr

Time taken to cover 300km = 300/(x + 5)

Given that time taken is 2hrs less from the previous time

⇒ 300x + 1500 – 300x = 2x (x + 5)

⇒ 1500 = 2x² + 10x

⇒ 750 = x² + 5x

⇒ x² + 5x – 750 = 0

⇒ x² + 30x – 25x – 750 = 0

⇒ x (x + 30) – 25 (x + 30) = 0

⇒ (x – 25) (x + 30) = 0

⇒ (x – 25) = 0 or (x + 30) = 0

∴ x = 25 or x = – 30

Since, speed can’t be negative.

Hence, the speed of the train is 25km/hr