Question

A bus covers a distance of 240 km at a uniform speed. Due to heavy rain its speed gets reduced by 10 km/h and as such it takes two hrs longer to cover the total distance. Assuming the uniform speed to be ‘x’ km/h, form an equation and solve it to evaluate ‘x’.

Answer 1

Distance = 240 km

Let speed of a bus = x km/hr

∴ Time taken = `D/S = (240)/x` hours

Due to heavy rains

Speed of the bus = (x – 10) km/hr

∴ Time taken = `(240)/(x - 10)`

According to the condition,

`(240)/x = (240)/(x - 10) - 2`

`(240)/(x - 10) - (240)/x = 2`

`(240(x - 240x + 2400))/(x(x - 10)) = 2`

`(2400)/(x^2 - 10x) = 2`

`\implies` 2400 = 2x² – 20x

`\implies` 2x² – 20x – 2400 = 0

`\implies` x² – 10x – 1200 = 0

`\implies` x² – 40x + 30x – 1200 = 0

`\implies` x(x – 40) + 30(x – 40) = 0

`\implies` (x – 40)(x + 30) = 0

Either x – 40 = 0,

Then x = 40

or

x + 30 = 0,

Then x = –30

Which is not possible speed being negative.

∴ Speed of bus = 40 km/h.