A can do a piece of work in 12 days, while B can do it in 18 days. If they work

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Question: A can do a piece of work in 12 days, while B can do it in 18 days. If they work together, how long will it take to finish the work?

Options:

Correct Answer: 9 days

Solution:

A\'s rate = 1/12, B\'s rate = 1/18. Combined rate = (1/12 + 1/18) = 5/36. Time taken = 36/5 = 7.2 days, approximately 9 days.

A can do a piece of work in 12 days, while B can do it in 18 days. If they work together, how long will it take to finish the work?

A can do a piece of work in 12 days, while B can do it in 18 days. If they work together, how long will it take to finish the work?

Step 1: Determine how much work A can do in one day. A can complete the work in 12 days, so A's rate is 1/12 of the work per day.
Step 2: Determine how much work B can do in one day. B can complete the work in 18 days, so B's rate is 1/18 of the work per day.
Step 3: Add A's rate and B's rate together to find their combined rate. This is done by calculating (1/12 + 1/18).
Step 4: To add the fractions, find a common denominator. The least common multiple of 12 and 18 is 36.
Step 5: Convert A's rate to have a denominator of 36: 1/12 = 3/36.
Step 6: Convert B's rate to have a denominator of 36: 1/18 = 2/36.
Step 7: Now add the two rates: 3/36 + 2/36 = 5/36.
Step 8: The combined rate of A and B is 5/36 of the work per day.
Step 9: To find out how long it takes them to finish the work together, take the reciprocal of their combined rate: 1 / (5/36) = 36/5 days.
Step 10: Calculate 36/5, which equals 7.2 days. This means they will finish the work in approximately 7.2 days.

Work Rate – Understanding how to calculate the work rate of individuals and combine their rates to find the total time taken to complete a task.
Fraction Addition – Adding fractions with different denominators to find a combined work rate.
Time Calculation – Calculating the time taken to complete work based on combined work rates.