Question 923774
Let x=amount of time it takes both conveyor belts working together to move 1000 bushels of corn
Then both conveyor belts working together moves corn at the rate of 1000/x bushels per minute
Large conveyor belt moves corn at the rate of 1/9 bushel per minute
Small conveyor belt moves corn at the rate of 1/14 bushel per minute
Sooo, our equation to solve is
1/9 +1/14 =1000/x multiply both sides by 126x
14x+9x=126,000
23x=126,000
x=(126,000/23) minutes=~~~~ 5478.261 minutes
CHECK---We'll deal in fractions.  That will eliminate round off errors.
In (126,000/23) minutes, large conveyor moves (126,000/23)(1/9) bushels of corn
In (126,000/23) minutes, small conveyor moves (126,000/23)(1/14) bushels of corn
(126,000/23)(1/9)+(126,000/23)(1/14)=?1000 bushels
(14000/23)+(9000/23)=1000
23000/23=1000
1000=1000

Hope this helps--ptaylor