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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.
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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`
`(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.
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