Question

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

Answer 1

distance = 360 km
..
let speed be x
then time taken = d/r
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.

Answer 2

Answer:

Step-by-step explanation:

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

Time taken to cover 360 km =  360/x hr

Time taken to cover 360 km at new speed = 360/x + 5 hr

According to the Question,

⇒ 360/x - 360/ x + 5 = 1

⇒ 360 (x + 5 - x)/x(x + 5) = 1

⇒ 360 (5) = x² + 5x

⇒ 1800 = x² + 5x

⇒ x² + 5x - 1800 = 0

⇒ x² + 45x - 40x - 1800 = 0

⇒ x (x + 45) - 40( x + 45) = 0

⇒ (x + 45) (x - 40) = 0

⇒ x = - 45, 40 (Speed cannot be negative)

⇒ x = 40 km/hr.

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