Math Question

Question

I just got accepted to the police academy and they have physical entrance standards I have to meet on day 1. They are as follows;

1 minute push-ups (26), 1 minute sit-ups (35), 1.5 mile run (13.62 minutes) and 300 meter sprint (62 seconds).

These are all Men 30% Standards, however, I do not need to hit these marks as long as I average 30% all together. So my question is If I were to crank out 40 push-ups (14 more then what is required) and 40 sit-ups (5 more then what is required) and I meet my mark with the 300 meter sprint how much additional time will I have for the 1.5 mile run to keep my average at 30%? Remember my average has to be 30% across the board.

Thank you,
David

Answer 1

Hi David, congratulations on you appointment. If I understand what you mean by the 30% level, then the following would be true.

 

100% level for push-ups would be about 115 push-ups. Your level, at 40 push-ups, would be about the 46% level.

 

100% level for sit-ups would be about 117 set-ups. Your level, at 35 sit-ups, would be about the 34% level.

 

You could meet the 30% level for the 300 meter sprint.

 

We need to find the missing average for the 1.5 mile run that would give you the 30% across the board. We do that by finding the average. Average is the sum of the individual events divided by 4. 

 

In this case, we know the average, but are missing one of the four event's number. We will let x represent the missing event's value.

 

30% = (46% + 34% + 30% + x%) / 4

 

Solve for x:

 

x = 120% - 110%, or you would have to complete the 1.5 mile run at the 10% level to average 30% across the board.

 

Based on the information provided, the 100% level for the 1.5 run is about 8 minutes. You would have to run the 1.5 mile run in about 15 minutes to be at the 10% level.

 

By doing the extra push-ups and sit-ups, you would gain about 1.4 minutes, which could be added to the 13.62 minutes.

 

Questions?