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Time & Work
· Examples✏️ Worked Examples — Step by Step
E1
EasyA 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?
💡 Find each person's daily rate (1/days), add the rates, then take the reciprocal.
👁 Show 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
✅7.2 days (36/5 days)
E2
MediumA tap fills a tank in 6 hours. Another tap fills it in 4 hours. If both taps are open together, how long to fill the tank?
💡 Same concept as time & work — each tap's rate is 1/hours.
👁 Show Solution
Step 1 — Rates Tap A = 1/6 per hour Tap B = 1/4 per hour Step 2 — Combined = 1/6 + 1/4 = 2/12 + 3/12 = 5/12 per hour Step 3 — Time = 1 ÷ (5/12) = 12/5 = 2.4 hours ✅ Answer: 2.4 hours (2 hours 24 minutes)
✅2.4 hours
E3
ChallengingA alone takes 10 days to do a job. A and B together take 6 days. How many days does B alone take?
💡 Find combined rate first, subtract A's rate to get B's rate, then invert.
👁 Show Solution
Step 1 — Combined rate (A+B) = 1/6 per day Step 2 — A's rate = 1/10 per day Step 3 — B's rate = 1/6 − 1/10 = 5/30 − 3/30 = 2/30 = 1/15 per day Step 4 — B alone takes = 1 ÷ (1/15) = 15 days ✅ Answer: B takes 15 days alone
✅15 days