Question 1206862: In 8 minutes, a conveyor belt can move 1,000 bushels of corn into a storage bin. A smaller belt can move 1,000 bushels to the storage bin in 14 minutes. If both belts are used, how long will it take to move 1,000 bushels to the storage bin?
Found 3 solutions by greenestamps, math_tutor2020, MathTherapy: Answer by greenestamps(13198) (Show Source): Answer by math_tutor2020(3816) (Show Source):
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Answer: 5.090909 minutes approximately
The "09" decimal portion repeats forever.
This is equivalent to the mixed number 5 & 1/11 minutes.
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Explanation
The LCM of 8 and 14 is 56 because:
8*14/2 = 56
where the "divide by 2" portion is the GCF of 8 and 14.
LCM = x*y/GCF
Conveyor A moves 1000 bushels of corn in 8 minutes.
If it keeps this same rate then it moves 7*1000 = 7000 bushels in 7*8 = 56 minutes.
Conveyor B moves 1000 bushels of corn in 14 minutes.
If it keeps this same rate then it moves 4*1000 = 4000 bushels in 4*14 = 56 minutes.
The key is to get both conveyors moving some amount of corn in the same amount of time.
Combine those amounts:
A+B = 7000+4000 = 11000
11,000 bushels of corn are moved in 56 minutes when the conveyor belts work together.
This assumes neither conveyor belt hinders the other.
The combined unit rate would be 11000/56 = 1375/7 = 196.42857 bushels per minute approximately.
Then,
rate*time = amountDone
time = amountDone/rate
time = (1000 bushels)/( 1375/7 bushels per min)
time = (1000*7/1375) minutes
time = (56/11) minutes
time = 5.090909090909 minutes approximately
The "09" part repeats forever.
If you want the answer as a mixed number then,
5.090909090909 = 5 & 1/11
Answer by MathTherapy(10551) (Show Source):
You can put this solution on YOUR website!
In 8 minutes, a conveyor belt can move 1,000 bushels of corn into a storage bin. A smaller belt can move 1,000 bushels to the storage bin in 14 minutes. If both belts are used, how long will it take to move 1,000 bushels to the storage bin?
As the 1,000 bushels is considered a SINGLE job, you CERTAINLY don't need to include the 1,000 bushels
in your calculations as the other person did.
Let the time it takes both belts to do the 1 job (move 1,000 bushels into the storage bin), be T.
Since the faster belt takes 8 minutes to do the job, it does of the job in 1 minute
Since the slower belt takes 14 minutes to do the job, it does of the job in 1 minute
We then get:
7T + 4T = 56 ----- Multiplying by LCD, 56T
11T = 56
Time it takes both belts to do the job (move 1,000 bushels into the storage bin), or 
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