A can complete a task in 18 days, B can complete it in 27 days. How long will th

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Question: A can complete a task in 18 days, B can complete it in 27 days. How long will they take to complete the task together?

Options:

Correct Answer: 9 days

Solution:

A\'s rate = 1/18, B\'s rate = 1/27. Combined rate = 1/18 + 1/27 = 1/10. They will finish the task in 10 days.

A can complete a task in 18 days, B can complete it in 27 days. How long will they take to complete the task together?

A can complete a task in 18 days, B can complete it in 27 days. How long will they take to complete the task together?

Step 1: Determine A's rate of work. A can complete the task in 18 days, so A's rate is 1/18 of the task per day.
Step 2: Determine B's rate of work. B can complete the task in 27 days, so B's rate is 1/27 of the task per day.
Step 3: Add A's rate and B's rate together to find their combined rate. This is 1/18 + 1/27.
Step 4: To add the fractions, find a common denominator. The least common multiple of 18 and 27 is 54.
Step 5: Convert A's rate to the common denominator: 1/18 = 3/54.
Step 6: Convert B's rate to the common denominator: 1/27 = 2/54.
Step 7: Now add the two rates: 3/54 + 2/54 = 5/54.
Step 8: The combined rate of A and B is 5/54 of the task per day.
Step 9: To find out how long it takes them to complete the task together, take the reciprocal of their combined rate: 1 / (5/54) = 54/5 days.
Step 10: Simplify 54/5 days to get 10.8 days.

Work Rate – Understanding how to calculate individual work rates and combine them to find the total work rate when multiple workers are involved.
Fraction Addition – Adding fractions with different denominators to find a common work rate.