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A fast train takes 3 hours less than a slow train for a journey of 900 km. If the speed of the slow train is 10 km/hr less than that of the fast train, then what is the speed of the fast train?

A fast train takes 3 hours less than a slow train for a journey of 900 km. If the speed of the slow train is 10 km/hr less than that of the fast train, then what is the speed of the fast train? Correct Answer <span style="">60 km/hr</span>

Given:

A fast train takes 3 hours less than a slow train for a journey of 900 km

The speed of the slow train = 10 km/hr less than that of the fast train

Formula used:

Time = Distance/Speed

Calculation:

Let the speed of slow train be x km/hr

Then, speed of fast train be (x + 10) km/hr

Time taken by slow train to cover 900 km = (900/x) hrs

Time taken by fast train to cover 900 km = 900/(x + 10) hrs

According to the question

⇒ (900/x) – (900/x + 10) = 3

⇒ 9000/x2 + 10x = 3

⇒ 3(x2 + 10x) = 9000

⇒ x2 + 10x – 3000 = 0

⇒ x2 + 60x – 50x – 3000 = 0

⇒ x(x + 60) – 50(x + 60) = 0

⇒ (x – 50), (x + 60) = 0

⇒ x = 50, -60

Hence, the speed of fast train is (x + 10) = (50 + 10) = 60 km/hr

∴ The speed of fast train is 60 km/hr

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