Answer:
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
