A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working together and A quits 10 days before the project is completed, in how many days will the project be completed?

18 days
27 days
26.67 days
16 days

Correct answer: 18 days

Solution

A’s rate is $1/20$ and B’s rate is $1/30$, so together they work at $1/12$ per day. If the project takes $T$ days, then A works for $T-10$ days and B for $T$ days, giving $(T-10)/20 + T/30 = 1$. Solving gives $T = 18$ days.

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