Question

if the speed of car is increased by 10 km/have, it takes 1 hrs less to cover a distance of 300 km. find the original speed of car

Answer 1

let the initial speed of the car be x kilometre per hour. Then,
new speed of the car will be x + 10 kilometre per hour.
Given, distance travelled by car is 300 km.
now time taken by the car at initial speed is t
= 300/x
again time taken by the car at new speed, t'
= 300/x + 10
and t - t' = 10
So, 300/x - 300/x + 10 = 1
=> 300x + 3000 - 300x / x² + 10x = 1
=> 3000 = x² + 10x
=> x² + 10x - 3000 = 0
=> x² + 60x - 50x -3000 = 0
=> x(x + 60) -50(x + 60) = 0
=> (x + 60) (x - 50) = 0
=> x = -60 or 50
So, x = 50 kmph as speed can't be in negative.
So the negative value of x is not valid.
Hence the speed of the car is 50 km per hour