The distance between two oppositely traveling objects is diminishing at a rate equal to the sum of the rates of the two moving objects, because they are closing in on each other. Since Jeff is traveling at 30 mph and Tim is traveling at 20 mph, the distance between them is closing at a rate of 30 + 20 = 50 mph .
Now we want to substitute our given distance, 120 miles, and our rate, 50 mph, into the rate formula to find time it takes for Jeff and Tim to meet.
Distance = Rate × Time
Rearranging this formula to solve for Time, we get:
Time = 2.4 hours
0.4 hours is 60 × 0.4 = 24 minutes. So Time = 2 hours and 24 minutes.
Since the bicyclists begin at 6 a.m. and it takes them 2 hours and 24 minutes to meet, then they meet at 8:24 a.m. The correct answer is C.