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Question
By increasing the speed of a car by 10 km/hr, the time of journey for a distance of 72 km. is reduced by 36 minutes. Find the original speed of the car.
Solution
Let original speed be x km/hr.
∴ Time = `(72)/x "hr"`.
New speed = x + 10 km/hr.
∴ New time = `(72)/(x + 10)"hr".`
Difference in time = 36 mins.
∴ `(72)/x - (72)/(x + 10) = (36)/(60)`
`(72x + 720 - 72x)/(x(x + 10)) = (3)/(5)`
5 x 720 = 3 (x2 + 10x)
1,200 = x2 + 10x
x2 + 10x - 1,200 = 0
x2 + 40x - 30x - 1,200 = 0
x (x + 40) - 30 (x + 40) = 0
(x - 30) (x + 40) = 0
∴ x = 30
as x = -40 is not acceptable
∴ Original speed = 30km/hr.
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