Question

To collect data on the signal strengths in a neighborhood, Tracy must drive from house to house and take readings. She has a graduate student, Dave, to assist her. Tracy figures it would take her eight hours to complete the task working alone, and that it would take Dave 12 hours if he completed the task by himself. How long will it take Tracy and Dave to complete the task together

Answer 1

Working together, they can complete the task in 4 hours and 48 minutes.

What is the concept of time and work?

A certain amount of time (T) is taken to complete a certain work (W). The number of units of work done per unit time is called the rate of work (R). Hence, Work (W) = Rate (R) Time (T) Whenever some work is done, the total work itself can be taken as one unit.

Tracy needs 8 hours to complete the task.

Then we can find the ratio of work over time as:

1 task/8 hours = 1/8 task per hour.

This means that she can complete 1/8 of the task per hour.

Dave needs 12 hours to complete the task, then his ratio is:

1 task/12 hours = 1/12 task per hour.

This means that he can complete 1/12 of the task in one hour.

If they work together, then the ratios can be added:

R = $\frac{1}{8}$ +  $\frac{1}{12}$

  = $\frac{3+2}{24}$

  = $\frac{5}{24}$

So, working together, in one hour they can complete  $\frac{5}{24}$ of the task, now we can find the number of hours needed to complete the task as:

$\frac{5}{24}$×$x$= 1 task

x = $\frac{24}{5}$ hours = 4.8 hours

knowing that an hour is 60 minutes, then 0.8 of an hour is 60*0.8 = 48 minutes.

Then x = 4 hours and 48 minutes.

To learn more about Time and work from the given link:

brainly.com/question/16900783

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