if wayne completed a task in one hour and sarah completed a task in two hours, how long will they take if they work together?

Every hour Wayne completes 1 task, and Sarah completes (1/2) task (simply take the reciprocal). Together, in 1 hour they will complete 3/2 tasks. Therefore, to complete 1 task, it takes them 2/3 hours.

To find out how long Wayne and Sarah will take if they work together, you can use the concept of work rates. Wayne completes the task in 1 hour, which means his work rate is 1 task per hour. Similarly, Sarah completes the task in 2 hours, so her work rate is 1/2 task per hour.

To determine how long they will take together, you can add their work rates. In this case, 1 task per hour + 1/2 task per hour equals 1.5 tasks per hour. This means that they can complete 1.5 tasks in one hour if they work together.

Now, to find the time it takes for them to complete the entire task, you need to divide the total task by their combined work rate. Since they can complete 1.5 tasks in one hour, we can set up the equation:

1.5 tasks / 1 hour = x tasks / t hours,

where x represents the total number of tasks they need to complete and t represents the time it will take for them to complete it together.

To solve for t, you can cross multiply:

1.5t = 1 * x

Divide both sides of the equation by 1.5 to solve for t:

t = x / 1.5

This means they will take x divided by 1.5 hours to complete the task together.