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’.

Answer 1

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`