Final answer:
The time it takes for both conveyor belts to move 100 pounds of aluminum to the storage area when used together is approximately 1.56 minutes. This is found by adding the rates of the two belts together and dividing the total weight by this combined rate.
Step-by-step explanation:
Conveyor Belt Problem
To solve the problem of how long it takes for two conveyor belts to move recyclable aluminum to a storage area when used together, we can find the rates at which they work and then combine these rates to find the combined rate. The first conveyor belt can move 100 pounds in 2 minutes, so its rate is 100 pounds per 2 minutes or 50 pounds per minute. The smaller conveyor belt moves 100 pounds in 7 minutes, so its rate is roughly 14.29 pounds per minute.
When both conveyor belts are used together, their combined rate is the sum of their individual rates:
50 lbs/min + 14.29 lbs/min = 64.29 lbs/min.
To find out how long it takes to move 100 pounds of aluminum using both belts, we divide the total amount of aluminum by the combined rate:
100 lbs / 64.29 lbs/min = 1.56 minutes.
Therefore, it will take approximately 1.56 minutes to move the cans to the storage area using both conveyor belts.