an experienced computer technician can set up a network in 12 hours. it would take an intern 20 hours to set…

an experienced computer technician can set up a network in 12 hours. it would take an intern 20 hours to set up the same network. if they work together, how long will it take to set up the network? if the experienced technician and intern work together, then we assume that the they work is the same. done rate time part of job experienced x intern x

an experienced computer technician can set up a network in 12 hours. it would take an intern 20 hours to set up the same network. if they work together, how long will it take to set up the network? if the experienced technician and intern work together, then we assume that the they work is the same. done rate time part of job experienced x intern x

Answer

Explanation:

Step1: Calculate individual work - rates

The experienced technician can set up the network in 12 hours. So the rate of work of the experienced technician is $\frac{1}{12}$ of the job per hour. The intern can set up the network in 20 hours. So the rate of work of the intern is $\frac{1}{20}$ of the job per hour.

Step2: Calculate combined work - rate

When they work together, their combined rate of work is the sum of their individual rates. Let the combined rate be $r$. Then $r=\frac{1}{12}+\frac{1}{20}$. First, find a common denominator, which is 60. So $\frac{1}{12}+\frac{1}{20}=\frac{5}{60}+\frac{3}{60}=\frac{5 + 3}{60}=\frac{8}{60}=\frac{2}{15}$ of the job per hour.

Step3: Calculate the time taken when working together

We know that rate $\times$ time = work. Let the time taken when they work together be $t$ hours and the work is 1 job. Since $r=\frac{2}{15}$ and work = 1, and $r\times t=1$, then $t=\frac{1}{r}$. Substituting $r = \frac{2}{15}$, we get $t=\frac{15}{2}=7.5$ hours.

Answer:

7.5 hours