If A can complete a task in 10 hours and B can do it in 15 hours, how much time

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Question: If A can complete a task in 10 hours and B can do it in 15 hours, how much time will they take to complete it together?

Options:

Correct Answer: 6 hours

Solution:

A\'s rate = 1/10, B\'s rate = 1/15. Together = 1/10 + 1/15 = 5/30 = 1/6. They will take 6 hours.

If A can complete a task in 10 hours and B can do it in 15 hours, how much time will they take to complete it together?

If A can complete a task in 10 hours and B can do it in 15 hours, how much time will they take to complete it together?

Step 1: Determine A's work rate. A can complete the task in 10 hours, so A's rate is 1 task per 10 hours, which is 1/10.
Step 2: Determine B's work rate. B can complete the task in 15 hours, so B's rate is 1 task per 15 hours, which is 1/15.
Step 3: Add A's and B's work rates together. This means we calculate 1/10 + 1/15.
Step 4: To add the fractions, find a common denominator. The least common multiple of 10 and 15 is 30.
Step 5: Convert A's rate to have a denominator of 30. 1/10 = 3/30.
Step 6: Convert B's rate to have a denominator of 30. 1/15 = 2/30.
Step 7: Now add the two rates: 3/30 + 2/30 = 5/30.
Step 8: Simplify 5/30 to 1/6. This means together they complete 1/6 of the task in 1 hour.
Step 9: To find out how long it takes them to complete the whole task together, take the reciprocal of 1/6, which is 6 hours.

Work Rate – Understanding how to calculate the combined work rate of two individuals working together.
Fraction Addition – Applying the concept of adding fractions to find the total work done together.