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.

(iv) 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.

Answer:

Let take speed of the train = x km/h

And time taken by train in normal speed  = y hours

A train travels a distance of 480 km at a uniform speed.

Distance = speed  × time

So we get

 x*y = 480                   …..(1)

. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance

New speed  = x – 8 km/h

Time taken = y + 3 hours

Use same formula again

Distance = speed × time

or,  (x- 8) × (y + 3)  = 480

    xy + 3x -8y – 24  = 480

plug xy = 480 we get

  480 + 3x – 8y – 24   = 480

  3x – 8y – 24            = 0

Find the value of y here

             -8y = 24 – 3x

Divide by – 8 we get

y = -3 + 3/8x

Plug this value in equation first we get

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

-3x + 3/8 x² = 480

Multiply by 8 we get

-24 x +  3x² = 3840

Divide by 3 we get

x² – 8x  = 1280

x² – 8x  - 1280 =0