A person P can complete a project in 24 days, and the person Q can complete it in 36 days. They work together for 4 days, after which Q leaves. In how many days will P complete the remaining work? (Give your answer rounded off to two decimal places.)
17.33 days
P's one day work \(= \dfrac{1}{24}\) and Q's one day work \(= \dfrac{1}{36}\).
Combined one day work \(= \dfrac{1}{24} + \dfrac{1}{36} = \dfrac{3+2}{72} = \dfrac{5}{72}\).
Work done in 4 days \(= 4 \times \dfrac{5}{72} = \dfrac{20}{72} = \dfrac{5}{18}\).
Remaining work \(= 1 - \dfrac{5}{18} = \dfrac{13}{18}\).
Time taken by P alone \(= \dfrac{13}{18} \div \dfrac{1}{24} = \dfrac{13 \times 24}{18} = 17.33\) days.
Hence, P will complete the remaining work in 17.33 days.
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