Alice can complete a digital artwork project in 15 days, while Bob can finish the same project in 30 days. They work together for 3 days before Alice leaves the project. In how many more days will Bob finish the remaining work alone?
Correct Answer :
21 days
Solution :
The correct answer is 21 days.
Step 1: Determine individual work rates per day.
Let the total project work be equal to 1 unit.
Alice can complete the project in 15 days, so Alice's 1-day work rate is:
Bob can complete the project in 30 days, so Bob's 1-day work rate is:
Step 2: Find their combined 1-day work rate.
When Alice and Bob work together, the portion of work they complete in 1 day is:
Step 3: Calculate the work completed in 3 days.
Alice and Bob work together for 3 days, so the fraction of work completed is:
Step 4: Calculate the remaining work.
The fraction of the work left to be finished is:
Step 5: Calculate the time taken by Bob to finish the remaining work alone.
Bob works at a rate of of the project per day. The number of days Bob requires to finish of the work is:
Therefore, Bob will finish the remaining work alone in 21 days.
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