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Question
A car covers a distance of 400 km at a certain speed. Had the speed been 12 km/h more, the time taken for the journey would have been 1 hour 40 minutes less. Find the original speed of the car.
Solution
Let x km/h be the original speed of the car.
We know that,
Time taken = `"Distance"/"Speed"`
It is given that the car covers a distance of 400 km with the speed of x km/h.
Thus, the time taken by the car to complete 400 km is t = `400/x`
Now, the speed is increased by 12 km.
Increased speed = (x + 12) km/h
Also given that, increasing the speed of the car will decrease the time taken by 1 hour 40 minutes.
Hence,
`400/x - 400/(x + 12)` = 1 hour 40 minutes
`=> 400/x - 400/(x + 12)` = `1 40/60`
`=> (400(x + 12) - 400x)/(x(x + 12)) = 1 2/3`
`=> (400x + 4800 - 400x)/(x(x + 12)) = 5/3`
`=> 4800/(x(x + 12)) = 5/3`
`=>` 3 × 4800 = 5 × x × (x + 12)
`=>` 14400 = 5x2 + 60x
`=>` 5x2 + 60x – 14400 = 0
`=>` x2 + 12x – 2880 = 0
`=>` x2 + 60x – 48x – 2880 = 0
`=>` x(x + 60) – 48(x + 60) = 0
`=>` (x + 60)(x – 48) = 0
`=>` x + 60 = 0 or x – 48 = 0
`=>` x = – 60 or x = 48
Since, speed cannot be negative, we reject – 60.
Hence, the original speed of the car is 48 km/h.
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