Question 630731
A group of 40 workers  can finish digging a tunnel in 12 days. how many workers can finish the job in 8 days.
<pre>
First way:  The least common multiple of 12 days and 8 days is 24 days.

>>...A group of 40 workers  can finish digging a tunnel in 12 days...<<

Therefore half as many workers (20 workers) could dig it in twice as many
days (24 days).

Therefore it would take 3 times as many workers (60 workers) to dig it
in one-third of 24 days (8 days).

Answer: 60 workers.


Second way:

<pre>
Use the job-worker-time formula, which is:

{{{(W[1]T[1])/J[1]}}}{{{""=""}}}{{{(W[2]T[2])/J[2]}}}

where

W<sub>1</sub> = the number of workers in the first situation.
T<sub>1</sub> = the number of time units (days in this case) in the first situation.
J<sub>1</sub> = the number of jobs in the first situation.

W<sub>2</sub> = the number of workers in the second situation.
T<sub>2</sub> = the number of time units (days in this case) in the second situation.
J<sub>2</sub> = the number of jobs in the second situation.

W<sub>1</sub> = 40            W<sub>2</sub> = the unknown quantity     
T<sub>1</sub> = 12            T<sub>2</sub> = 8 
J<sub>1</sub> = 1             J<sub>2</sub> = 1

[There was only 1 tunnel, so the number of jobs in both situations is 1.

{{{(W[1]T[1])/J[1]}}}{{{""=""}}}{{{(W[2]T[2])/J[2]}}}

{{{(40*12)/1}}}{{{""=""}}}{{{(W[2]*8)/1}}}

     480 = 8W<sub>2</sub>
      
Divide both sides by 8

      60 = W<sub>2</sub>

Answer: 60 workers.

Edwin</pre>