Question

When running a half marathon (13.1 miles), it took David 7 minutes to run from mile marker 1 to mile marker 2, and 18 minutes to run from mile marker 2 to mile marker 4. How long did it take David to run from mile marker 1 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?

Answer 1

Answer:

It took 25 minutes to run from marker 1 to marker 4

a) Average speed from 1 to 4: 0.273 miles/min

b) Average speed needed from 9 to 13.1 : 0.1 miles/min

Step-by-step explanation:

First we know that it took 7 minutes to run from marker 1 to 2 and then 18 additional minutes to run from marker 2 to 4... so, it took (7+18) minutes to run from marker 1 to 4 => 7+18 = 25 minutes.

a) The average speed formula between to points xa and xb is:

• (xb-xa)/(t2-t1)

where t1 and t2 are the times it took to reach xa and xb.

In this case xa= 1 mile; xb= 4 miles and t1= 7 min while t2= 18 min.

so Average speed= (4-1) miles/(18-7)min= 3/11 miles/ min= 0.273 miles per minute

b) If we want to use the average formula betwwen the two points 9 and 13.1, in this case:

xa= 9 miles    t1= 69 minutes

xb= 13.1 miles  t2= 110 minutes

Then Average speed= (13.1-9) miles/(110-69) minutes= 4.1 miles/41 minutes= 0.1 miles per minute