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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. - Mathematics

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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.

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#### Solution

Let original speed of train = x km/h

We know,

Time = distance/speed

We have

Time taken by train = 360/x hour

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

It is given that,

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

360/x - 360/(x + 5) = 48/60 = 4/5

360(1/x - 1/(x +5)) = 4/5

360 xx 5/4 (5/(x^2 + 5x)) = 1

450 × 5 = x2 + 5x

x2 + 5x – 2250 = 0

x = (-5 +- sqrt(25 + 9000))/2

= (-5 +- sqrt(9025))/2

= (-5 +- 95)/2

= – 50, 45

But x ≠ – 50 because speed cannot be negative

So, x = 45 km/h

Hence, original speed of train = 45 km/h

Concept: Nature of Roots
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#### APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 4 Quadatric Euation
Exercise 4.4 | Q 4 | Page 42

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