Question

A train travels 480 km at a uniform speed. if the speed had been 10 km/h more it would have take 4 hours less for the same journey find the speed of the train​

Answer 1

first time I was solving the problem

so answer is 16km

Answer 2

Answer:

speed of the train = 30km/h

Step-by-step explanation:

given, distance = 480 km,

consider speed of the train be x km/h

speed = $\frac{distance}{time}$

then, time taken to travel distance of 480 km = $\frac{480}{x}$ hour

when speed is increased to (x+10) km/h, time taken to cover the same distance = $\frac{480}{x+10}$ hour

when speed is increased to (x+10) km/h time is reduced by 4 hour for the same distance

⇒ $\frac{480}{x+10}$ = $\frac{480}{x} - 4$

⇒ $\frac{480}{x+10}$ = $\frac{480 - 4x}{x}$

⇒ 480x = (480 - 4x) (x+10)

⇒480x = 480x + 4800 - 4x² -40x

⇒ 4x² + 40x - 4800 = 0

⇒ x² +10x -1200 = 0

⇒ x = 30,-40

time taken to travel at 30 km/h = $\frac{480}{x} = \frac{480}{30}$ = 16 hour

time taken to travel at speed  40 km/h = $\frac{480}{x+10} = \frac{480}{40}$ = 12 hour

16 -12 = 4 hour. there is a reduction by 4 hour when speed was 10km/h more

hence, speed of the train = 30km/h