(Q9) Represent the following situations in the form of quadratic equations:

(iv)A train travels a distance of 480km at a uniform speed. If the speed had been 8km/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 the speed of the train be x km/h.

Then time taken to travel a distance of 480km =
distance
speed
 =
480
x
If the speed is 8km/h less, then time needed to cover the same distance would be
480
x -
By problem
480
x-
 -
480
x
 = 3
480[
1
x-
 -
1
x
] = 3
480[
x-(x-)
x(x-)
] = 3
480[x-x+]
x2-x
 = 3

x2-x =

x2-x- = 0

where x is the speed of the train.