Terrance and jesse are training for a long distance race. terrance trains at the rate of 6 miles every half an hour and jesse trains at the rate of 2 miles every 15 minutes. how long will each person take a rum of a total of 50 miles at the given rate ,

"Terrance trains at the rate of 6 miles every half an hour and Jesse trains at the rate of 2 miles every 15 minutes.  How long will each person take to run of a total of 50 miles at the given rates?"

I will treat this as two problems:  Terrance's case and Jesse's case.

Terrance's rate is (6/.5) mph, or 12 mph, and Jesse's is (2/0.25) mph, or 8 mph.

At this rate, Terrance can run 50 miles in how many hours?  Divide 50 miles by 12 mph:  (50/12) hours, or (25/6) hours, or 4 hours 10 minutes.

At his won rate, Jesse can run 50 miles in (50 mi) / 8mph         hours,
which reduces to 25/4 hours, or 6 1/4 hours.