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Question
A car made a run of 390 km in ‘x’ hours. If the speed had been 4 km/hour more, it would have taken 2 hours less for the journey. Find ‘x’.
Solution
Let the original speed of the car be y km/hr
We know
`"Speed" = "Distance"/"Time"`
∴ `y = 390/x`
`=> x = 390/y` ...(1)
New speed of the car = (y + 4) km/hr
New time taken by the car to cover 390 km = `390/(y + 4)`
From the given information,
`390/y - 390/(y + 4) = 2`
`(390y + 1560 - 390y)/(y(y + 4)) = 2`
`780/(y^2 + 4y) = 1`
y2 + 4y – 780 = 0
y2 + 30y – 26y – 780 = 0
y(y + 30) – 26(y + 30) = 0
(y + 30)(y – 26) = 0
y = –30, 26
Since, time cannot be negative, so y = 26
From (1), we have
`x = 390/y = 390/26 = 15`
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