Question

in 2 minutes, a conveyor belt moves 500 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 5 minutes. if both belts are used, find how long it takes to move the cans to the storage area.

Answer 1

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.