Sum

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’.

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#### 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`

`y^2 + 4y - 780 = 0`

`y^2 + 4y - 780 = 0`

`y^2 + 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`

Concept: Quadratic Equations

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