If the speed of a train is increased by 20 km/hr, then it travels 300km less distance in 2.5 hours. How much time will the train take to cover a distance of 192km?
Answers
Answer:
let the speed of train be x
it increase=x+20
time=300/x+20
b
3.2 hours time the train will take to cover a distance of 192km.
Let the original speed be x km/hr
Distance is 300km.
Time taken is = Distance/Speed = 300/x hours
If speed is increased by 20km/hr, new speed is = (x+20) km/hr
Time taken now to cover 300 km is = 300/(x+20) hours
This difference in time is equal to 2.5 hours. So,
300/x - 300/(x+20) = 2.5
⇒ (300x + 6000 - 300x )/(x[x+20]) = 5/2
⇒ 5x² + 100x = 12000
⇒ 5x² + 100x - 12000
⇒ x² + 20x - 2400 = 0 [Dividing both sides by 5]
⇒ x² + 60x - 40x - 2400 = 0
⇒ x(x+60) -40(x+60) = 0
⇒ (x+60)(x-40) =0
By zero product rule, x = -60 cant be true as speed cant be negative.
So, x = 40.
The original speed was 40 km/hr
New speed = 40 + 20 = 60 km/hr
Time taken to cover 192 km is = 192/60 hours
= 3.2 hours.