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

Given

The train travels at a uniform speed of 360 km.

It would have taken 48 minutes less to travel the same distance if its speed were 5 km/h more

Find out

We have to determine the original speed of train

Solution

Let the original speed of train = s km/h

We know that

Time = distance/speed

According to the question, we have,

Time is taken by train = 360/s hour

And, Time taken by train its speed increase 5 km/h = 360/( s + 5)

It is given that,

Time taken by train in first – time taken by train in 2nd case = 48 min = 48/60 hour

360/s – 360/(s +5) = 48/60 = 4/5

360(1/s – 1/(s +5)) = 4/5

360 ×5/4 (5/(s² +5s)) =1

450 × 5 = s² + 5s

s² +5s -2250 = 0

s = (-5± √ (25+9000))/2

= (-5 ±√ (9025) )/2

= (-5 ± 95)/2

= -50, 45

But s ≠ -50 because speed cannot be negative

So, s = 45 km/h

Answer

Hence, original speed of train = 45 km/h

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