A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/hr less, then it would have taken 3 hours more to cover the same distance. The original speed of the train is?

By Ishita Gupta|Updated : May 17th, 2023

A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/hr less, then it would have taken 3 hours more to cover the same distance. The original speed of the train is?

The average speed of a train can be calculated by dividing the total distance covered by the train and the time taken by the train to cover the distance. By applying this formula one can find that the original speed of the train is 40 km/hr.

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Distance of Train

The total motion covered by the train regardless of the direction is known as Distance. The distance can be described as how much distance the train covered despite any start or end point.

Speed of Train

Speed is a measurable quantity that measures the ratio of the distance traveled by train to the time required to travel that distance. Speed is divided into four types- Uniform, Variable, Instantaneous and Average Speed.

Time of Train

Time can be stated as the dimension based on the advancement of any system. The SI unit of time is seconds. Time can be expressed as seconds, minutes, hours, days, weeks, months, and years.

Solution

Let the original speed be v km/hr

Let’s assume that it covers 480 km in time t hrs

So,

Speed = Distance/ Time

Equation 1: V = 480/t

If it travels at a speed of 8km/hr, it takes 3 more hours to cover the same distance

Equation 2: V-8= 480/ t+3 = v= (480/t+3 +8)

Equating equations 1 and 2

480/t+3 + 8 = 480/t

480/t+3 = 480/t-8 = 480-8t/t

480t = (480 - 8t) (t+3)

480t = 480t + 1440 - 8t2 - 24t

8t2 +24t - 1440 = 0

t2 + 3t - 180 = 0

(t-15)(t+12) = 0

t = - 15 or 12

As time cannot be negative, t= 12 hrs

Hence,

v= 480/t = 480/12 = 40 km/hr

The original speed of the train is 40 km/hr

Summary