When running a half marathon (13.1 miles), it took Grant 7 minutes and 45 seconds to run from mile marker 1 to mile marker 2, and 19 minutes and 15 seconds to run from mile marker 2 to mile marker 4.

A) As Grant's distance from the starting line increased from 1 to 4 miles, what average speed (in miles per minute) did he run?

B) 69 minutes after starting the race Grant passed mile marker 9. What average speed in miles per minute will Grant need to run, from mile marker 9 to the end of the race, to meet his goal to complete the 13.1 mile half-marathon in 110 minutes?

The length of the half marathon is 13.1 miles. it took Grant 7 minutes and 45 seconds to run from mile marker 1 to mile marker 2. Converting 7 minutes and 45 seconds to minutes, it becomes

7 + 45/60 =7.75 minutes

Speed = distance/time

Therefore, his speed from mile marker 1 to mile marker 2 is

1/7.75 = 0.129 miles per minute

He spent 19 minutes and 15 seconds to run from mile marker 2 to mile marker 4. Converting 19 minutes and 15 seconds to minutes, it becomes

19 + 15/60 =19.25 minutes

Therefore, his speed from mile marker 2 to mile marker 4 is

2/19.255 = 0.104 miles per minute

A) his average speed from miles 1 to 4 would be

(0.129 + 0.104)/2 = 0.1165 miles per minute.

B) after running the 9th mile, distance remaining would be

13.1 - 9 = 4.1 miles

Time left to complete the race would be

110 - 69 = 41 minutes

Average speed needed to complete the race would be

4.1/41 = 0.1 miles per minute.