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Question

A train covers a distance of 90km at a uniform speed.Had the speed been 15kmphr more, it would have taken 30 minutes less for the journey.Find the original speed of the train.

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Solution

Let the original speed of the train be xkmphr

time take to cover a distance of 90km=90xhrs.

The new speed of the train=x+15kmph

new time taken to cover 90km=90x+15hrs.
Since the train takes 30 minutes

90x90x+15=12

90(x+15xx2+15x)=12

90(15x2+15x)=12

2700x215x=0

x2+15x2700=0

(x+60)(x45)=0

x=60 or x=45 but x cannot be negative.

x=45

Hence the original speed of the train =45kmph

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