Peggy rode her bike to the farm. Mike decided to go by car. It took Mike half an hour to get there. Peggy made the trip in 2 hours. How far was the farm if mike was traveling 36mph faster than Peggy?

The farm was 24 miles away.

Step-by-step explanation:

In order to solve this question we will attribute variables to the problem. We have:

The speed at wich Peggy was going it'll be "v_peggy";

The speed at wich Mike was going it'll be "v_mike".

The distance they travelled will be "d".

The problem told us that the speed Mike travelled was 36 mph faster than Peggy, so:

v_mike = v_peggy + 36

The distance of said course is given by the speed and the the time it took to complete it. So we have:

d = 0.5*v_mike and d = 2*v_peggy

The distances are the same, so:

0.5*v_mike = 2*v_peggy

Using the equation that relates Mike's speed to Peggy's, we have:

(v_peggy+36) * 0.5 = 2*v_peggy

0.5*v_peggy + 36*0.5 = 2*v_peggy

2*v_peggy - 0.5*v_peggy = 18

1.5*v_peggy = 18

v_peggy = 12 mph

Now we can compute the distance that is:

d = (12) * 2 = 24 miles