Question

A train takes 2 hours less for a journey of 300km if its speed is increased by 5km/hr from its usual speed.Find the usual speed of the train.

Answer 1

time= distance/speed
let unusual speed be x
so (300/x)-(300/x+5)=2
300{(x+5)-x}=2(x+5)x
1500=2x(x+5)
x(x+5)=750
(x^2)+5x-750=0
from this equation, we can find the two zeroes for the equation as -30 and 25
as speed can never be negative,
so x=25 kmph

Answer 2

Answer:

Step-by-step explanation:

Solution :-

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

Time taken to cover 300 km = 300/x hr

Time taken with increased speed = 300/x + 5 hr

According to the Question,

⇒ 300/x + 300/(x + 5) = 2

⇒ 300x + 1500 - 300x/x(x + 5) = 2

⇒ 1500/x² + 5x = 2

⇒ 1500 = 2x² + 10x

⇒ 2x² + 10x - 1500 = 0

⇒ x² + 5x - 750 = 0

⇒ x² + 30x - 25x - 750 = 0

⇒ x(x + 30) - 25(x + 30) = 0

⇒ (x + 30) (x - 25) = 0

⇒ x = - 30, 25 (As x can't be negative)

⇒ x = 25 km/h

Hence,  the usual speed of the train is 25 km/h.