If a train travelled 5 km/hr faster, it would take one hour less to travel 210 km. The speed of the train is _____. [ 3 marks]

Open in App

Solution

Let the speed of the train be x km/hr.
Distance travelled = 210 km

Time taken to travel 210 km = $\frac{210}{x}$ hours

When the speed is increased by 5 km/h, the new speed is (x+5)

Time taken to travel 210 km with the new speed is $\frac{210}{x + 5}$ hours [1 mark]

According to the question,
$\frac{210}{x} - \frac{210}{x + 5} = 1$
$\Rightarrow 210 (x + 5) - 210 x = x (x + 5)$
$\Rightarrow 210 x + 1050 - 210 x = x^{2} + 5 x$
$\Rightarrow x^{2} + 5 x - 1050 = 0$
$\Rightarrow (x + 35) (x - 30) = 0$
$\Rightarrow x = - 35, 30$ [1 mark]

The speed cannot be negative. Thus, the speed of the train is 30 km/hr [ 1 mark]

Suggest Corrections

Similar questions

A train, travelling at a uniform speed for $360 k m$ , would have taken $48$ minutes less to travel the same distance if its speed were $5 k m / h r$ more. Find the original speed of the train.

Q. If a train travelled 5 km/hr faster, it would take one hour less to travel 210 km. The speed of the train is : _____

[3]

If a train travelled 5 km/hr slower, it would take one hour more to travel 210 km. The speed of the train is :

Q. A train travels 360 km in a certain amount of time. If the train were 5 km/hr faster then it would take 1 hour less. Find the original speed of the train.

Q. A faster train takes one hour less than a slower train for a journey of

200 k m

. If the speed of slower train is

10 k m / h r

less than that of faster train, find the speeds of two trains.

Join BYJU'S Learning Program