Question

A and B can do a work in 12 days and 15 days respectively. How long will they take to complete the work if they work together?

• A. 6\(\frac{2}{3}\) days
• B. 7 days
• C. 8 days
• D. 5 days

Hint:

In work and time problems, calculate each person’s work rate (work per day = 1/time taken). Add the rates to find the combined rate, then take the reciprocal to find the total time. Use the least common multiple (LCM) of individual times to simplify calculations or verify results. If the result is not a whole number, check the options for the closest reasonable value or consider if the problem assumes completion in whole days.

Answer 1

The Correct Option is A

The objective is to determine the duration for A and B to finish the task when collaborating.

1. Foundational Principles:

- Work Rate Definition: A's daily contribution to the task is \( \frac{1}{12} \) if A completes it in 12 days.
- Correspondingly, B's daily contribution is \( \frac{1}{15} \).
- The collective daily work rate when working together is the sum of their individual daily rates.
- The total time to complete the task collaboratively is the inverse of their combined daily work rate.

2. Provided Data:

- Time for A to complete the work = 12 days
- Time for B to complete the work = 15 days

3. Calculation of Combined Work Rate and Time:

\[ \text{Combined work rate} = \frac{1}{12} + \frac{1}{15} = \frac{5}{60} + \frac{4}{60} = \frac{9}{60} = \frac{3}{20} \] \[ \text{Time taken} = \frac{1}{\text{Combined work rate}} = \frac{1}{\frac{3}{20}} = \frac{20}{3} = 6\frac{2}{3} \text{ days} \]

Conclusion:

Working in unison, A and B will finalize the work in 6\(\frac{2}{3}\) days, equivalent to 6 days and 8 hours.