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 8 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

Tracy and Dave  together complete the task in $\frac{24}{5}$ hours

Given Tracy alone  take 8 hours to complete work and dave alone take 12 hours to complete the work.

Let's say together they worked in x hours

⇒in 1 hour they worked  $\frac{1}{x}$th part of the work

Tracy herself worked 8 hours to complete the whole task

⇒ in 1 hour Tracy completes $\frac{1}{8}$th part of the task

Dave himself worked 8 hours to complete the whole task

⇒ in 1 hour Dave completes $\frac{1}{12}$th part of the task

By proportions

⇒$\frac{1}{8}$+$\frac{1}{12}$=$\frac{1}{x}$ { using operation addition}

⇒ x=  $\frac{24}{5}$  

Therefore,Tracy and Dave  together complete the task in $\frac{24}{5}$ hours

Learn more about hour here:

brainly.com/question/13533620

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