SOLUTION: In 9 ​minutes, a conveyor belt moves 300 pounds of recyclable aluminum from the delivery truck to a storage area. A smaller belt moves the same quantity of cans the same dist

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: In 9 ​minutes, a conveyor belt moves 300 pounds of recyclable aluminum from the delivery truck to a storage area. A smaller belt moves the same quantity of cans the same dist      Log On


   

Question 1080135: In 9 ​minutes, a conveyor belt moves 300 pounds of recyclable aluminum from the delivery truck to a storage area. A smaller belt moves the same quantity of cans the same distance in 45 minutes. If both belts are​ used, find how long it takes to move the cans to the storage area.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The rate for the large conveyor belt is:
+300%2F9+=+100%2F3+ pounds/min
The rate for the smaller belt is:
+300%2F45+=+20%2F3+
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Let +t+ = time in minutes for the 2 belts
used together to move +300+ pounds
Add their rates to get rate working together
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+100%2F3+%2B+20%2F3+=+300%2Ft+
Multiply both sides by +3t+
+100t+%2B+20t+=+900+
+120t+=+900+
+t+=+7.5+
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Both belts used together take 7 min 30 sec to
move 300 pounds of cans
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check:
+100%2F3+%2B+20%2F3+=+300%2Ft+
+100%2F3+%2B+20%2F3+=+300%2F7.5+
+33.333+%2B+6.667+=+40+
+40+=+40+
OK