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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

Solution:

We have to find the original speed of the train.

We know, time = distance / speed

Let the original speed be x.

Given, time taken at first = 360/x

Time taken at increased speed = 360/(x+5)

360/x - 360/(x+5) = 48/60

360[(x+5)-x] = (48/60)[x(x+5)]

360[x + 5 - x] = 4/5[x(x+5)]

360(5) = 4/5(x² + 5x)

90(25) = x² + 5x

x² + 5x - 2250 = 0

On factoring,

x² + 50x - 45x - 2250 = 0

x(x + 50) - 45(x + 50) = 0

(x - 45)(x + 50) = 0

Now, x - 45 = 0

x = 45

Also, x + 50 = 0

x = -50

Since speed cannot be negative, x = -50 is neglected.

Therefore, the original speed of the train is 45km/hr.

✦ Try This: A train, travelling at a uniform speed for 670 km, would have taken 56 minutes less to travel the same distance if its speed were 9 km/h more. Find the original speed of the train

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 4

NCERT Exemplar Class 10 Maths Exercise 4.4 Problem 4

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

Summary:

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. The original speed of the train is 45km/hr

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