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Men–days–hours (Time & work, pipes & cisterns)
M₁D₁H₁ / W₁ = M₂D₂H₂ / W₂
Where: D₁ = days (group 1), D₂ = days (group 2), H₁ = hours per day (group 1), H₂ = hours per day (group 2), M₁ = men (group 1), M₂ = men (group 2), W₁ = work (group 1), W₂ = work (group 2)
Solved example
Given: D_2 = 7, H_1 = 5, H_2 = 10, M_1 = 4, M_2 = 3, W_1 = 8, W_2 = 6
Find: D_1 (days (group 1))
- Formula: D₁·H₁·M₁/W₁ = D₂·H₂·M₂/W₂
- Rearranged for D₁: D₁ = D₂·H₂·M₂·W₁/(H₁·M₁·W₂)
- Substitute the values: D₁ = 10·3·7·8/(4·5·6)
- Result: D₁ = 14
Answer: D_1 = 14
Calculator
How to calculate Men–days–hours (Time & work, pipes & cisterns)
- Write down the formula: M₁D₁H₁ / W₁ = M₂D₂H₂ / W₂.
- Note the known values (D₂, H₁, H₂, M₁, M₂, W₁, W₂).
- Substitute them and simplify to find D_1.
- Use the calculator above to solve for any letter.
Frequently asked questions
What is the formula for Men–days–hours (Time & work, pipes & cisterns)?
The formula is M₁D₁H₁ / W₁ = M₂D₂H₂ / W₂, where D₁ = days (group 1), D₂ = days (group 2), H₁ = hours per day (group 1), H₂ = hours per day (group 2), M₁ = men (group 1), M₂ = men (group 2), W₁ = work (group 1), W₂ = work (group 2).
What is Men–days–hours (Time & work, pipes & cisterns) when D_2 = 7, H_1 = 5, H_2 = 10, M_1 = 4, M_2 = 3, W_1 = 8, W_2 = 6?
D_1 = 14. Substitute the values into M₁D₁H₁ / W₁ = M₂D₂H₂ / W₂ and simplify.