Represent the following situations in the form of quadratic equations:

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

Dear student

Let us consider,
The speed of train = x km/h
And Time taken to travel 480 km = 480/x km/hr
As per second condition, the speed of train = (x - 8) km/h
Also given, the train will take 3 hours to cover the same distance.
Therefore, time taken to travel 480 km = 480/(x+3) km/h
As we know, Speed × Time = Distance
Therefore,
(x - 8)(480/(x + 3) = 480
⇒ 480 + 3x – 3840/x - 24 = 480
⇒ 3x – 3840/x = 24
⇒ 3x 2 - 8x - 1280 = 0
Therefore, the speed of the train,
satisfies the quadratic equation,
3x 2 - 8x - 1280 = 0,
which is the representation of the problem mathematically

Thanks