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.

Answer 2

The time taken by 3 electricians is 9 hours and 33 minutes.

What is inverse variation?

"Two quantities follow inverse variation if one quantity is directly proportional to the reciprocal of the other quantity. This means that an increase in one quantity leads to a decrease in the other while a decrease in one quantity leads to an increase in the other".

For the given situation,

Number of electricians be 'x'

Time required be 'y'

Proportionality constant be 'k'

Inverse variation can be represented as $x = k(\frac{1}{y})$

Equation 1:

Number of electricians = 7

Time required = 4 hours

k can be find by,

$x = k(\frac{1}{y})$

⇒$7=k(\frac{1}{4} )$

⇒$k=28$

Equation 2:

Number of electricians = 3

Time required = y

$x = k(\frac{1}{y})$

⇒$3 = 28(\frac{1}{y} )$

⇒$y=\frac{28}{3}$

⇒$y=9.33$

Hence we can conclude that the time taken by 3 electricians is 9 hours and 33 minutes.

Learn more about inverse variation here

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