Question

The time required to process a shipment of goods at Walmart varies with the number of goods and inversely with the number of workers assigned. If 15,000 items can be processed by 8 workers in 10 hours, then how long would it take 12 workers to process 20,000 items?

Answer 1

I will assume that

The time required to process a shipment of goods at Walmart varies directly with the number of goods and inversely with the number of workers assigned

Let

y ---->time required to process a shipment in hours

x ---> number of goods

z ---> number of workers assigned

so

the equation is of the form

$y=\frac{kx}{z}$

where

K is the constant of proportionality

step 1

Find out the value of k

we have

x=15,000

y=10 hours

z=8

substitute in the above equation

$10=\frac{k(15,000)}{8}_{}$

Solve for K

$\begin{gathered} k=\frac{10\cdot8}{15,000} \\ k=\frac{2}{375} \end{gathered}$

step 2

Find out the value of y

we have

z=12

x=20,000

substitute in the equation

$y=\frac{2}{375}\cdot\frac{x}{z}$$\begin{gathered} y=\frac{2}{375}\cdot\frac{20,000}{12} \\ y=8.9\text{ hours} \end{gathered}$

The answer is 8.9 hours