Question

If the speed of a car is increased by 10 km per hr, it takes 18 minutes less to cover a distance of 36 km. Find the speed of the car.

Answer 1

Let the speed of the car be x km/hr.

Distance = 36 km

Time taken to cover a distance of 36 km = 36/x hrs

`("Time" = "Distance"/"Speed")`

New speed of the car = (x + 10) km/hr

New time taken by the car to cover a distance of 36 km = `36/(x + 10)` hrs

From the given information, we have:

`36/x - 36/(x + 10) = 18/60`

`(36(x + 10) - 36x)/(x(x + 10)) = 3/10`

`(36x + 360 - 36x)/(x(x + 10)) = 3/10`

`360/(x(x + 10)) = 3/10`

3x² + 30x = 3600

3x² + 30x – 3600 = 0

x² + 10x – 1200 = 0   ...(Dividing by 3)

x² + 40x – 30x – 1200 = 0  

x(x + 40) – 30(x + 40) = 0

(x + 40)(x – 30) = 0

x = – 40, 30

But speed cannot be negative.

So, x = 30.

Hence, the original speed of the car is 30 km/hr.