Represent the 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 3 hours more to cover the same distance. We need to find the speed of the train.

Let the speed of train = x Km/h
Total distance = 480 Km
Therefore, time taken = 480/x hours
If the speed had been 8 Km/h less, than time taken = 480/x-8 hours
According to the questions,
480/x-8 – 480/x = 3
⇒ 480x – 480(x – 8)/(x – 8)x = 3
⇒ 480x – 480x + 3640 = 3(x – 8)x
⇒ 3640 = 3x² – 24x
⇒ 3x² – 24x – 3640 = 0
Hence, the speed of train satisfies the quadratic equation 3x² – 24x – 3640 = 0.