Question

Represent the following situation in the form of a quadratic equation.

A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.

A train covers a distance of 480 km at a uniform speed. If the speed had been 8 km/hr less then it would have taken 3 hours more to cover the same distance. Find the usual speed of the train. 

Answer 1

Step 1: Write the time equation

Original time = `480/x`

New time = `480/(x-8)`

`480/(x-8) = 480/x + 3`

Step 2: Solve the equation

`480/(x-8) - 480/x = 3`

`480 ((x-(x-8))/(x(x-8))) = 3`

`480(8/(x(x-8))) = 3`

`3840/(x(x-8)) = 3`

3840 = 3x (x − 8)

3840 = 3x² − 24x

1280 = x² − 8x

x² − 8x − 1280 = 0

Step 3: Solve the quadratic

x² − 8x − 1280 = 0

x² − 40x + 32x − 1280 = 0

(x − 40) (x + 32) = 0

x = 40