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Question

A car covers a distance of 240 km with some speed. If the speed is increased by 20km/hr, it will cover the same distance in 2 hours less. Find the speed of the car.

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Solution

Let the speed of the car be x km/hr.
Then, the time taken by the car to complete 240 km will be Distance Speed = 240x hr.
Now, if the speed of the car is increased by 20 km/hr, then the time taken to complete 240 km will be Distance Speed =240x+20 hr.
By the given condition, we get:
240x-240x+20=2240x+20-xxx+20=220x2+20x=1120
x2 + 20x = 2400
x2 + 20x – 2400 = 0
On splitting the middle term 20x as 60x – 40x, we get:
x2 + 60x – 40x – 2400 = 0
x(x + 60) – 40(x + 60) = 0
(x + 60)(x – 40) = 0
x + 60 = 0 or x – 40 = 0
x = – 60 or x = 40
Since x is the speed of the car, which cannot be negative, x = 40.
Thus, the speed of the car is 40 km/hr.

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