Question

Direct and inverse variation

Answer 1

Answer:

4 workers can do the job in 18 days.

Step-by-step explanation:

The number of days d varies inversely as the number of workers.

We can write it as: $d\: \alpha\: \frac{1}{w} \\d=\frac{k}{w}$

where k is constant of proportionality

We are given: If it takes 9 days for 8 workers to complete the job, then how many workers would it take to do the job in 18 days.

d = 9, w = 8

d = 18, w =?

First we will find value of k when d = 9, w =8

$d=\frac{k}{w}\\9=\frac{k}{8}\\k=9*8\\k=72$

The value of k, will remain same as it is constant.

We get k = 72.

So, Now we have d = 18, k = 72 and we need to find w

$d=\frac{k}{w}\\18=\frac{72}{w}\\18w=72\\w=\frac{72}{18}\\w=4$

So, 4 workers can do the job in 18 days.