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Time & Work
· Formula🧮 Formula Reference Sheet
Rate = 1 ÷ Days_to_complete Combined Rate = Rate_A + Rate_B Days Together = 1 ÷ (Rate_A + Rate_B) Shortcut (2) = (A × B) ÷ (A + B) Shortcut (3) = ABC ÷ (AB + BC + CA)
⚡ Example per formula
Rate = 1 ÷ Days_to_complete
↳A finishes in 10 days → Rate = 1/10 per day
Combined Rate = Rate_A + Rate_B
↳1/10 + 1/15 = 3/30 + 2/30 = 5/30 per day
Days Together = 1 ÷ (Rate_A + Rate_B)
↳1 ÷ (5/30) = 30/5 = 6 days
Shortcut (2) = (A × B) ÷ (A + B)
↳(10 × 15) ÷ (10 + 15) = 150/25 = 6 days
Shortcut (3) = ABC ÷ (AB + BC + CA)
↳A=6, B=8, C=12 → (576) ÷ (48+96+72) ≈ 2.67 days
✏️ Worked Example
A can finish a job in 12 days. B can finish the same job in 18 days. If they work together, how many days will they take to finish the job?
👁 Show step-by-step solution
Step 1 — Find daily rates A's rate = 1/12 of the job per day B's rate = 1/18 of the job per day Step 2 — Combined rate = 1/12 + 1/18 = 3/36 + 2/36 = 5/36 of the job per day Step 3 — Days together = 1 ÷ (5/36) = 36/5 = 7.2 days ✅ Answer: 7.2 days
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Practice Exercises →
5 graded problems · AI checks each step