# 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.

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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 gety = -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 getx2 – 8x = 1280x2 – 8x - 1280 =0

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 gety = -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 getx2 – 8x = 1280x2 – 8x - 1280 =0