A fast train takes hours less than a slow train for a journey of . If the speed of the slow train is less than that of the first train, find the speeds of the two trains.
Step 1: Determining the quadratic equation in
Let the speed of the slow train be .
Then, the speed of the fast train will be .
The time taken by the slow train to cover a distance of is hours.
And the time taken by the fast train to cover a distance of is hours.
It is given that the fast train takes hours less than the slow train.
Step 2: Determining the speed of trains
By factorization method,
For splitting the middle term, i.e. , we need to find two numbers such that their sum is and the product is .
Such numbers can be and .
Since the speed of the train cannot be negative,
and
Therefore, the speeds of the slow train and fast train are and , respectively.