Question

If 12 assemblers can complete a certain job in 4 hours, how long will the same job take if the number of assemblers is cut back to 8?

Answer 1

We will use the nifty formula shown below to solve this rate-job problem.

`\text{RWT}=J`

Where

R is the rate

W is the number of workers

T is the time

J is the number of jobs

Here, it is given "12 assemblers can complete a certain job in 4 hours". Thus,

W = 12

J = 1

T = 4

Let's figure out the rate:

`\begin{gathered} \text{RWT}=J \\ R(12)(4)=1 \\ R(48)=1 \\ R=(1)/(48) \end{gathered}`

Now, we will again use the formula to see how long it will take "8 workers" to do the same job.

So,

W = 8

J = 1

T = ??

So,

`\begin{gathered} \text{RWT}=J \\ ((1)/(48))(8)T=1 \\ (8)/(48)T=1 \\ T=(1)/((8)/(48)) \\ T=(48)/(8) \\ T=6 \end{gathered}`Answer

6 hours