Final answer:
When both belts are used, it takes approximately 1.43 minutes (or 1 minute and 26 seconds) to move the cans to the storage area.
Step-by-step explanation:
Let's assume that the time taken by the larger conveyor belt to move the cans to the storage area is x minutes.
According to the given information, the larger belt moves 500 pounds of cans in 2 minutes, while the smaller belt moves the same quantity of cans in 5 minutes. This means that the larger belt is faster.
Using the concept of rates, we can set up the following equation:
Rate of larger belt = 500 pounds / 2 minutes = 250 pounds/minute
Rate of smaller belt = 500 pounds / 5 minutes = 100 pounds/minute
When both belts are used, the total rate is the sum of their individual rates:
Total rate = 250 pounds/minute + 100 pounds/minute
Total rate = 350 pounds/minute
Now, using the formula Time = Quantity / Rate, we can find the time taken to move the cans to the storage area:
x = 500 pounds / 350 pounds/minute
x = 1.43 minutes
Therefore, it takes approximately 1.43 minutes (or 1 minute and 26 seconds) to move the cans to the storage area when both belts are used.