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# A Train Covers a Distance of 90 Km at a Uniform Speed. Had the Speed Been 15 Km/Hour More, It Would Have Taken 30 Minutes Less for a Journey. Find the Original Speed of the Train. - Mathematics

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#### Question

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

#### Solution

Let the original speed of train be x km/hr. Then,

Increased speed of the train = (x + 15)km/hr

Time taken by the train under usual speed to cover 90 km = 90/xhr

Time taken by the train under increased speed to cover 90 km = 90/(x+15)hr

Therefore,

90/x-90/(x+15)=30/60

(90(x+15)-90x)/(x(x+15))=1/2

(90x+1350-90x)/(x^2+15x)=1/2

1350/(x^2+15x)=1/2

1350(2) = x2 + 15x

2700 = x2 + 15x

x2 + 15x - 2700 = 0

x2 - 45x + 60x - 2700 = 0

x(x - 45) + 60(x - 45) = 0

(x - 45)(x + 60) = 0

So, either

x - 45 = 0

x = 45

Or

x + 60 = 0

x = -60

But, the speed of the train can never be negative.

Hence, the original speed of train is x = 45 km/hr

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