Question

Runner A crosses the starting line of a marathon and runs at an average pace of 5.6 miles per hour. Half an hour later, Runner B crosses the starting line and runs at an average rate of 6.4 miles per hour. If the length of the marathon is 26.2 miles, which runner will finish ahead of the other? Explain.
Runner A; Runner B will not be able to catch Runner A in the time it takes Runner A to complete the 26.2 mile course.
Runner B; Runner B will catch up to runner A 3.5 hours after Runner A crosses the starting line.
Runner B; Runner B will pass Runner A and finish more than half an hour ahead of Runner A.
Runner B; Runner B will catch up to Runner A 4 hours after Runner A crosses the starting line.

Answer 1

Time it took runner A to complete the marathon = 26.2 / 5.6 = 4 hrs 41 mins
Time it took runner B to complete the marathon = 26.2 / 6.4 = 4 hrs 6 mins

Time it took runner B to complete the marathon relative to when runner A started = 30 mins + 4 hrs 6 mins = 4 hrs 36 mins

Therefore, runner B will finnish ahead of runner A.

Let x be the time the two runners are at the same point, then
5.6x + 5.6(0.5) = 6.4x
6.4x - 5.6x = 2.8
0.8x = 2.8
x = 2.8/0.8 = 3.5
Therefore, runner B will catch up with runner A 3.5 hours after runner A starts the race.
Runner B; Runner B will catch up to Runner A 3.5 hours after Runner A crosses the starting line.