Question

A train travels 180 km at a uniform speed. If the speed had been 9km per hour more,it would have taken 1hour less for the same journey. Find the speed of the train

Answer 1

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.

Answer 2

Answer:

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.