So let us set up the equations:
d = rt
d = 12t and plug in r = 12
so after t hours, the faster runner is 12t miles which is for the faster runner.
d = rt
d = 8t plug in r = 8
so after t hours, the slower runner has 8t miles.
Now if you want to get the distance, simply subtract:
12t – 8t = 4t
Since we need to get the distance of ¼ mile, meaning:
12t – 8t = ¼
= 4(12t – 8t) = 4 x 1/4 -> multiply both sides by the lcd to clear the fractions
= 48t – 32t = 1
=16t = 1
Get t by dividing both sides by 16 to isolate t.
So the answer is 1/16 which is about 0.0625.
