<PRE><B>Question 239421</B>
One conveyor belt can move 1000 boxes in 12 minutes.
 Another can move 1000 boxes in 10 minutes. 
If another conveyor belt is added and all three are used, the boxes are moved in 3 minutes. 
How long would it take the third conveyor belt alone to do the same job?
:
Let x = time required by the 3rd conveyor to move 1000 boxes
:
Let the completed job = 1; (moving 1000 boxes)
:
A shared work equation:
{{{3/12}}} + {{{3/10}}} + {{{3/x}}} = 1
Multiply equation by 60x to eliminate the denominators, results:
5x(3) + 6x(3) + 60(3) = 60x
:
15x + 18x + 180 = 60x
:
33x + 180 = 60x
:
180 = 60x - 33x
:
180 = 27x
x = {{{180/27}}}
x = 6{{{2/3}}} min
:
:
Check on a calc: enter (3/12) + (3/10) + (3/6.67) ~ 1 </PRE>