A runner runs the 40 miles from Marathon to Athens at a constant speed. Halfway through the run she injures her foot, and continues to run at half her previous speed. If the second half takes her 8 hours longer than the first half, how many hours did it take the runner to run the second half?
Choose the correct option
A) 10  B) 12  C) 16  D) 20  E) 24
The runner runs the first 20 miles at speed v and the second 20 miles at speed v/2.   The time T2 to run the second half must be twice the time T1 to run the first half.   T2 = 2*T1 = T1+8   T1 = 8 and so T2 = 16.   The answer is 16.
<result>C</result>
A runner runs the 40 miles from Marathon to Athens at a constant speed. Halfway through the run she injures her foot, and continues to run at half her previous speed. If the second half takes her 8 hours longer than the first half, how many hours did it take the runner to run the second half?