If a boiler room must have and FTE present at all times 24 hours per day 7 days a week how many FTE's are needed assuming 832 hours total paid time off per year?

The answer is 4.6 and you can get the answer in two similar ways:

First approach

24 hours a day for 7 days a week= 168 hours per week

168 hours per week for 52 weeks= 8736 hours per year

8736 hours a year in addition to the 832 hours off= 9568 hours total per year

9568 is the total hours needed by FTEs

FTEs work 40 hours a work week for 52 weeks=2080 hours a year.

9568 hours needed divided by the 2080 hours FTEs provide for a year= 4.6 FTEs needed

(24 x 7)= 168 hr/week

(168 x 52)= 8736 hr/yr

(8736 + 832)= 9568 hr/yr needed

(40 x 52)= 2080 hr/yr one FTE works

9568 / 2080= 4.6 FTEs

Second approach

24 hours a day for 365 days a year= 8760 hours per year

8760 hours per year in addition to the 832 hours off= 9592 hours total per year

9592 is the total hours needed by FTEs

FTEs work 40 hours a week.

40 hours a week divided by seven days a week= 5.714285714... hours per day (repeating decimals)

FTEs work 5.714285714... hours per day for 365 days a year= 2085.714285714... hours per year (repeating decimals)

9592 hours needed divided by the 2085.714285714... hours FTEs provide for a year= 4.59890410958904... FTEs (repeating decimals)

Approximately 4.6 FTEs needed

(24 x 365)= 8760

(8760 + 832)= 9592 hr/yr

(40 / 7)=5.714285714... hr/day

(5.714285714 x 365)= 2085.714285714... hr/yr one FTE works

(9592 / 2085.714285714)= 4.59890410958904... FTEs

Approximately 4.6 FTEs