A runner completes the first 10 laps of a 15-lap race at an average speed of 1 minute and thirty seconds per lap. How fast will the runner's average lap time need to be for the last five laps if they want to have average per-lap speed of one minute and twenty-five seconds for the entire race?

Velocity = 75 sec/lap

Step-by-step explanation:

First we must know how long it should take to complete all the laps.

15lap*(1min and 25sec per lap) = 15lap*(85sec/lap) =  21min and 15sec

if the first 10 laps have 1min + 30sec, then 10lap*(1min+30sec per lap) = 10lap*(90sec/lap) =900sec/(60sec/min)=15min

Then 21min+15sec - 15min = 6min +15sec This is the time in which you must take the last 5 laps to average 1 minute with 25 seconds throughout the race

so,  

6min + 15sec = 360sec +15sec = 375sec/5lap = 75sec/lap

Note: 15lap*(85sec/lap)= 1275sec/(60sec/min)=21.25 min= 21min + 0.25min*(60sec/min) =21min + 15sec

middle maybe?

step-by-step explanation: