If A can do a work in 15 days and B can do it in 20 days, how long will they tak

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Question: If A can do a work in 15 days and B can do it in 20 days, how long will they take to complete the work together?

Options:

Correct Answer: 10 days

Solution:

A\'s rate = 1/15, B\'s rate = 1/20. Combined rate = 1/15 + 1/20 = 1/12. They will complete the work in 12 days.

If A can do a work in 15 days and B can do it in 20 days, how long will they take to complete the work together?

If A can do a work in 15 days and B can do it in 20 days, how long will they take to complete the work together?

Step 1: Determine how much work A can do in one day. Since A can complete the work in 15 days, A's rate is 1/15 of the work per day.
Step 2: Determine how much work B can do in one day. Since B can complete the work in 20 days, B's rate is 1/20 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 1/15 + 1/20.
Step 4: To add 1/15 and 1/20, find a common denominator. The least common multiple of 15 and 20 is 60.
Step 5: Convert 1/15 to 4/60 and 1/20 to 3/60. Now add them: 4/60 + 3/60 = 7/60.
Step 6: The combined rate of A and B is 7/60 of the work per day.
Step 7: To find out how many days it will take them to complete the work together, take the reciprocal of their combined rate: 1 / (7/60) = 60/7 days.
Step 8: Calculate 60/7, which is approximately 8.57 days. Therefore, A and B together will complete the work in about 8.57 days.

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