Question

A bus covers a distance of 90 km at a uniform speed. Had the speed been `(15"km")/"hour"` more it would have taken 30 minutes less for the journey. Find the original speed of the bus

Answer 1

Let the original speed of the bus be “x” `"km"/"hr"`

Time taken to cover 90 km = `90/x`

After increasing the speed by `(15"km")/"hr"`

Time taken to cover 90 km = `90/(x + 15)`

By the given condition

`90/x - 90/(x + 15) = 1/2`

`(90(x + 15) - 90x)/(x(x + 15)) = 1/2`

90x + 1350 – 90x = `(x^2 + 15x)/2`

1350 = `(x^2 + 15x)/2`

2700 = x² + 5x

x² + 15x – 2700 = 0

(x + 60) (x – 45) = 0

x + 60 = 0 or x – 45 = 0

x = – 60 or x = 45

The speed will not be negative

∴ Original speed of the bus = `(45"km")/"hr"`