A can finish a job in 25 days, B can finish it in 30 days. How long will they ta

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Question: A can finish a job in 25 days, B can finish it in 30 days. How long will they take to finish the job together?

Options:

Correct Answer: 15 days

Solution:

A\'s rate = 1/25, B\'s rate = 1/30. Combined rate = 1/25 + 1/30 = 1/14. They will finish the job in 14 days.

A can finish a job in 25 days, B can finish it in 30 days. How long will they take to finish the job together?

A can finish a job in 25 days, B can finish it in 30 days. How long will they take to finish the job together?

Step 1: Determine how much of the job A can complete in one day. Since A can finish the job in 25 days, A's rate is 1/25 of the job per day.
Step 2: Determine how much of the job B can complete in one day. Since B can finish the job in 30 days, B's rate is 1/30 of the job per day.
Step 3: Add A's rate and B's rate together to find their combined rate. This is done by calculating 1/25 + 1/30.
Step 4: To add the fractions, find a common denominator. The least common multiple of 25 and 30 is 150.
Step 5: Convert A's rate to the common denominator: 1/25 = 6/150.
Step 6: Convert B's rate to the common denominator: 1/30 = 5/150.
Step 7: Now add the two rates: 6/150 + 5/150 = 11/150.
Step 8: The combined rate of A and B is 11/150 of the job per day.
Step 9: To find out how many days it will take them to finish the job together, take the reciprocal of their combined rate: 1 / (11/150) = 150/11 days.
Step 10: Simplify 150/11 to get approximately 13.64 days, which means they will finish the job in about 14 days.

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