Two marathon runners leave the starting gate, one running at 12mph and the other at 8 mph. if they maintain this pace, how long will it take for them to be a 1/4 mile apart

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.