Question

The time required to complete a job varies inversely as the number of people working. it took 4 hours for 7 electricians to wire a building. how long would it have taken 3 electricians to have done the job?

Answer 1

Let's assign variables

The time required to wire a building: y

The number of electricians to have done this job: x


y varies inversely as x

so that:
$y= k\frac{1}{x}$
where  k is the proportional constant


To calculate the value of k, plug in the values of x and y:
x=7
y=4

$4=k (\frac{1}{7}) \\~\\k=28$


Now, write down the relation between x and y:
$y=28x$


"how long would it have taken 3 electricians to have done the job?"
x=3
Let's find out y:
$y=(28) \frac{1}{3} = \frac{28}{3} =9 \frac{1}{3} =9.333333~~hr$

So it would take 9 hours and 20 minutes to have this job done.