Simran can finish a task in 4 days, while Tina can finish the same task in 8…

When two people work together, their combined rate of work is the sum of their individual rates of work. If a person alone completes a task in n days, that person's rate of work is 1/n of the task per day, and once the individual rates are added together, the time taken to finish the whole task together is the reciprocal of that combined rate.

1. Simran completes the task alone in 4 days, so Simran's rate of work is 1/4 of the task per day.

2. Tina completes the task alone in 8 days, so Tina's rate of work is 1/8 of the task per day.

3. Working together, their combined rate of work is 1/4 + 1/8 of the task per day. Using a common denominator of 8, this is 2/8 + 1/8 = 3/8 of the task per day.

4. The time taken to complete one whole task at a combined rate of 3/8 of the task per day is the reciprocal of that rate: 1 divided by 3/8, which is 8/3 days.

Check: in 8/3 days, Simran completes (8/3) multiplied by (1/4) = 2/3 of the task, and Tina completes (8/3) multiplied by (1/8) = 1/3 of the task. Together this is 2/3 + 1/3 = 1, that is exactly one whole task, confirming that the combined time of 8/3 days is correct.