A train travels 180km at a uniform speed. If the speed had been 9km/hr more, it would have taken 1 hour less for the same journey. Find the speed of the train.
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Let the speed of train be x km /h
Distance = 180 km
So, time = 180 / x
When speed is 9 km/h more, time taken = 180 / x+9
According to the given information:
180 / x - 180 / x+9 = 1
180 (x+9-x) / x(x+9) = 1
180 * 9 = x(x+9)
1620 = x2 + 9x
x2 + 9x - 1620 = 0
x2 + 45x - 36x - 1620 = 0
x(x+45) - 36(x+45) = 0
(x-36)(x+45) = 0
x = 36 or -45
But x being speed cannot be negative.
So, x = 36
Hence, the speed of the train is 36km/h.
Distance = 180 km
So, time = 180 / x
When speed is 9 km/h more, time taken = 180 / x+9
According to the given information:
180 / x - 180 / x+9 = 1
180 (x+9-x) / x(x+9) = 1
180 * 9 = x(x+9)
1620 = x2 + 9x
x2 + 9x - 1620 = 0
x2 + 45x - 36x - 1620 = 0
x(x+45) - 36(x+45) = 0
(x-36)(x+45) = 0
x = 36 or -45
But x being speed cannot be negative.
So, x = 36
Hence, the speed of the train is 36km/h.
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