What is the equation and solution for this word problem

Question

Jack has run 15 miles. His slowest time per mile was 9 minutes and 14 seconds. His fastest time for a mile was 6 minutes and 58 seconds. What is a reasonable estimate for how much time Jack has spent running the 15 miles

Answer 1

Without more information, you can only assume his average pace is the mid-point (or average) between his fastest and slowest time per mile.

 

slowest:  9 min 14 sec

fastest:   6 min 58 sec

 

convert both times to total secs:

9:14 = 9min x 60 sec/min + 14 sec = 554 sec

6:58 = 6min x 60 sec/min + 58 sec = 418 sec 

 

midpt we add the two times and divide by two.  (554 + 418)/2  = 486 sec  

 

if we use this as his average pace (486 sec/mile) x 15 miles = 7,290 sec to run 15 miles

 

we want to convert 7,290 sec  to hours, minutes, sec

 

1 hr = 3,600 sec   so  7,290/3600 = 2.025 hrs   

 

just use the whole number (2) for hours,

so subtract 2 (2.025-2) and the remainder, 0.025(hr) x 60 to get minutes = 1.5 minutes

 

just use the whole number (1) for minutes,

so subtract 1 (1.5-1) and the remainder, 0.5(min) x 60 to get seconds = 30 sec 

 

so, 7,290 seconds =  2 hrs, 1 min, 30 sec   which can be written as  2:01:30