If A can complete a task in 8 hours and B can complete it in 12 hours, how long

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Question: If A can complete a task in 8 hours and B can complete it in 12 hours, how long will it take them to complete the task together?

Options:

Correct Answer: 4.8 hours

Solution:

A\'s rate = 1/8, B\'s rate = 1/12. Together = 1/8 + 1/12 = 5/24. Time = 24/5 = 4.8 hours.

If A can complete a task in 8 hours and B can complete it in 12 hours, how long will it take them to complete the task together?

If A can complete a task in 8 hours and B can complete it in 12 hours, how long will it take them to complete the task together?

Step 1: Determine A's work rate. A can complete the task in 8 hours, so A's rate is 1 task per 8 hours, which is 1/8 of the task per hour.
Step 2: Determine B's work rate. B can complete the task in 12 hours, so B's rate is 1 task per 12 hours, which is 1/12 of the task per hour.
Step 3: Add A's and B's work rates together. This means we calculate 1/8 + 1/12.
Step 4: To add 1/8 and 1/12, find a common denominator. The least common multiple of 8 and 12 is 24.
Step 5: Convert 1/8 to a fraction with a denominator of 24. 1/8 = 3/24.
Step 6: Convert 1/12 to a fraction with a denominator of 24. 1/12 = 2/24.
Step 7: Now add the two fractions: 3/24 + 2/24 = 5/24.
Step 8: The combined work rate of A and B is 5/24 of the task per hour.
Step 9: To find out how long it takes them to complete 1 task together, take the reciprocal of their combined rate: 1 / (5/24) = 24/5 hours.
Step 10: Calculate 24/5, which equals 4.8 hours.

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