When running a marathon you heard the timer call out 12 minu

When running a marathon you heard the timer call out 12 minutes as you passed mile-marker 2. a. As you passed mile-marker 5 you heard the timer call out 32 minutes. How would you calculate your average speed in miles per minute from mile 2 to mile 5? b. Find this average speed. Your answer should be at least to the nearest hundredth of a mile per minute. c. Assume that you now start running at a constant speed that is equal to the average speed you computed in (b) above. How many miles did you cover as your time spent running increased from 35 minutes after the start of the race to 40 minutes after the start of the race? Your answer should be rounded to at least the nearest hundredth of a mile. d. If you passed mile marker 5 at 32 minutes, what average speed in miles per minute do you need to run for the remainder of the race to meet your goal to complete the 26.2 -mile marathon in 240 minutes? Your answer should be rounded to at least the nearest hundredth of a mile per minute.

Solution

b) average speed = ( 5- 2) / ( 32 - 12 )

= 3 / 20

= 0.15 miles / minute

c) speed = 0.15 mile / minute

distance covered in 35 minutes = 0.15*35 = 5.25 miles

distance covered in 40 minutes = 0.15* 40 = 6 miles

miles covered = 6 - 5.25 = 0.75 miles

d) total distance = 26.2 miles

total time = 240 minutes

distance left = 26.2 - 5 = 21.2

time left = 240 - 32 = 208

average speed = total distance / total time

average speed = 21.2 / 208 = 0.10 miles / min