Calculating Work Completion Time Together

To find the time it takes for A and B to complete the work together, we first determine their individual rates of work.

Work Rate of A

Person A finishes the work in 1170 days. Therefore, A's work rate is the fraction of the work done per day. Using LaTeX for the formula: Rate of A = $\frac{1}{\text{Total Time taken by A}}$ Rate of A = $\frac{1}{1170}$ work per day.

Work Rate of B

Similarly, Person B finishes the same work in 2340 days. Rate of B = $\frac{1}{\text{Total Time taken by B}}$ Rate of B = $\frac{1}{2340}$ work per day.

Combined Work Rate

When working together, their rates add up. The combined rate is: Combined Rate = Rate of A + Rate of B Combined Rate = $\frac{1}{1170} + \frac{1}{2340}$

To add these fractions, find a common denominator, which is 2340. Combined Rate = $\frac{2}{2340} + \frac{1}{2340}$ Combined Rate = $\frac{3}{2340}$ work per day.

Time to Complete Work Together

The total time taken to complete the work together is the reciprocal of the combined work rate. Time Together = $\frac{1}{\text{Combined Rate}}$ Time Together = $\frac{1}{\frac{3}{2340}}$ Time Together = $\frac{2340}{3}$ days.

Calculating the final value: Time Together = 780 days.

Therefore, working together, A and B will complete the same work in 780 days.