Topic 12 of 15, EHL Maths & Excel final (AP)
⏱
Work problems: rooms, workers, days and hours
In a work problem the work rate stays the same: rooms ÷ (workers × days × hours) is equal in both situations. Use the full row to find the rate, then solve for the one value that is missing.
When the exam asks for it
- “how many hours per day …”, “how many workers are needed …”, “how many days …”, “how many rooms can be cleaned …”
Formulas
Work rate (stays the same)
rate = Rooms1 / (Workers1*Days1*Hours1)Hours per day is missing
Hours2 = Rooms2*Workers1*Days1*Hours1 / (Rooms1*Workers2*Days2)Hours per day in Excel (row 3)
=A3*$B$2*$C$2*$D$2/($A$2*B3*C3)Workers are missing
Workers2 = Rooms2*Workers1*Days1*Hours1 / (Rooms1*Days2*Hours2)Workers in Excel (row 4)
=A4*$B$2*$C$2*$D$2/($A$2*C4*D4)Days are missing
Days2 = Rooms2*Workers1*Days1*Hours1 / (Rooms1*Workers2*Hours2)Days in Excel (row 5)
=A5*$B$2*$C$2*$D$2/($A$2*B5*D5)Rooms are missing
Rooms2 = Rooms1*Workers2*Days2*Hours2 / (Workers1*Days1*Hours1)Rooms in Excel (row 6)
=$A$2*B6*C6*D6/($B$2*$C$2*$D$2)Worked example
D3fx
=A3*$B$2*$C$2*$D$2/($A$2*B3*C3)| A | B | C | D | E | |
|---|---|---|---|---|---|
| 1 | Rooms to clean | Workers | Days | Hours per day | |
| 2 | 720 | 12 | 5 | 8.0 | |
| 3 | 675 | 10 | 6 | missing → 7.5 | |
| 4 | 1,080 | missing → 15 | 6 | 8.0 | |
| 5 | 810 | 9 | missing → 6 | 10.0 | |
| 6 | missing → 540 | 10 | 4 | 9.0 | |
| 7 |
Sheet1
⬇ Download practice ExcelExample, Practice and Answers sheets with working formulas. Free.
Step by step
- Rate from row 2720 / (12*5*8) = 1.5 rooms per worker per hour
=A3*$B$2*$C$2*$D$2/($A$2*B3*C3)hours per day: 675*12*5*8 / (720*10*6) = 7.5 hours=A4*$B$2*$C$2*$D$2/($A$2*C4*D4)workers: 1,080*12*5*8 / (720*6*8) = 15 workers=A5*$B$2*$C$2*$D$2/($A$2*B5*D5)days: 810*12*5*8 / (720*9*10) = 6 days=$A$2*B6*C6*D6/($B$2*$C$2*$D$2)rooms: 720*10*4*9 / (12*5*8) = 540 rooms
⚠ Exam traps
- More rooms means more hours; more workers or more days means fewer hours. Check that your answer moves the right way.
- Lock the full row with $ ($A$2, $B$2, $C$2, $D$2): it is the same reference row for every missing value.
- Put every known value of the second situation in the right place: the missing value never appears in its own formula.
- Hours per day and days are different things: 6 days of 8 hours is 48 hours, not 6 or 8.
Practice question
10 workers clean 600 rooms in 5 days working 6 hours per day. How many hours per day do 12 workers need to clean 840 rooms in 5 days?
Show answer
✓ 840*10*5*6 / (600*12*5) = 7 hours per day.
Stuck on this topic before your exam? We explain it one-to-one on your own Excel files, live online. Short crash courses before the EHL Maths & Excel final are possible on weekdays and weekends.
Book a lesson
Tell us your course, your exam date and the topics that worry you. We start with what matters most for your grade.
WhatsApp is preferred
The fastest way to book: send us a message and we usually answer the same day.
or email info@ytutor.net
Send a message
We answer by email or WhatsApp.