#### 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.

#### Solution

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`

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

`360/(x^2 + 10x) = 3/10`

`120/(x^2 + 10x) = 1/10`

`x^2 + 10x - 1200 = 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

Is there an error in this question or solution?

Solution 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. Concept: Quadratic Equations.