Question

A train travels 360km at uniform speed.If the speed had been 5km/h more ,it would have taken 1hr less for the same journey.find the speed of the train.

Answer 1

Let speed be x

T=360/x

If speed is increased by 5 km/h

speed will be (x+5)km/h

distance is the same

T= 360/(x+5)

time with original speed - time with increased speed = 1

360/x - 360/(x+5)=1

LCD= x(x+5)

(360(x+5)-360x) /x(x+5)=1

360x+1800-360x=x(x+5)

x^2+5x = 1800

x^2+5x-1800=0

x^2+45x-40x-1800=0

x(x+45)-40(x+45)=0

(x-40)(x+45)=0

x= 40 mph the original speed ,i;e speed of train is 40 mph

Hope you got your answer

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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