Algebra-2

Let's assume the speed of Jack is  miles per hour. Then the speed of Tom is  miles per hour.

We use the formula  (where  is time,  is distance, and  is speed) to find the time taken by each rider.

For Jack, who travels a distance  miles at a speed , the time taken  hours.

For Tom, who travels a distance  miles at a speed , the time taken  hours.

We are given that Tom takes 2 hours less than Jack to complete his ride. So we can set up the following equation:

Substituting the expressions for  and  we found earlier:

 
To get rid of the denominators, we multiply through by :

Expand the brackets:

Simplify the left side:

Rearrange the equation to get a quadratic equation in standard form:

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