Question

a train travels 360 km at a uniform speed.if speed has been 5 km/h more ,it would have taken 1 hour less for same journey.find the speed of the train.

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Answer 1

let the speed of train = x km/h
time taken = 360/x hour
if speed has been 5 km/h more,
speed = x+5
time taken will be = 360/(x+5) hour

According to the question,

$\frac{360}{x} -\frac{360}{x+5}= 1 \\ \\ \frac{360*5+360x-360x}{x(x+5)} =1 \\ \\ 1800=x(x+5) \\ \\ x^{2} +5x-1800=0$
Solving we get x= 40 km/h

Answer 2

Answer:

=) Let the original speed of the train be x km/h.

Time taken to cover a distance of 360 km =  360/x hours.

New speed of the train = (x+5) km/h.

Time taken to cover a distance of 360 km at new speed = 360/x+5 hours.

Since, the train takes 1 hour less time,

∴ 360/x - 360/ x+5 = 1

⇒360 (x+5-x)/x(x+5) = 1

⇒360 (5) = x^2 + 5x

⇒1800 = x^2 + 5x

⇒x^2 + 5x - 1800 = 0

⇒x^2 + 45x - 40x - 1800 = 0

⇒x (x+45) - 40( x +45) = 0

⇒(x+45) (x-40) = 0

⇒x = (-45), 40

But since speed cannot be in negative.

∴ x = 40 km/hr.

Hence, the original speed of the train is 40 km/h

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