Question

a passenger train takes 2 hours less for a journey of 300 kilometre if its speed is increased by 5 kilometre per hour from its usual speed find its usual speed​

Answer 1

Its usual speed is 25 kilometre/hour

Explanation:

Let the usual time duration for a journey of 300 km. = t

Let the usual speed = v

The parameters given are;

The time duration for the 300 km. journey at increased speed = t - 2

The increased speed of the passenger train = v + 5

Distance, d = Speed, v × Time, t

Therefore, we have;

v × t = 300

∴ t = 300/v

Also (v + 5)×(t - 2) = 300

Substituting the value of t = 300/v, we have;

(v + 5)×(300/v - 2) = 300

`- (2 \cdot v^2 - 290 \cdot v - 1500)/(v) = 300`

Which gives;

2·v² + 10·v - 1500 = 0

Which is equivalent to v² + 5·v - 750 = 0

Therefore we have;

(v + 30)·(v - 25) = 0 whereby v = -35 or 25 km/h

v = Natural number = 25 km/hour

Therefore its usual speed is 25 kilometre/hour.