Question

In 2 minutes, a conveyor belt moves 800 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 3 minutes. If both belts are used, find how long it takes to move the cans to the storage area.

Answer 1

It will take 1.2 minutes if the two belts are used together

Here, we will be working with calculating joint rate

The rate for the bigger belt is;

`\frac{800\text{ lbs}}{2\text{ minutes }}\text{ = 400 lbs/min}`

For the smaller belt, the rate is;

`\frac{800\text{ lbs}}{3\text{ minutes }}\text{ = }(800)/(3)\text{ lbs/min}`

Now, since we are combining both belts, we will be combining their rates

So, we simply divide the total weight by the addition of the rates

Thus, we have this as;

`\begin{gathered} (800)/(400+(800)/(3)) \\ =\text{ }(800)/((1200+800)/(3)) \\ \\ =\text{ }(800)/((2000)/(3)) \\ =\text{ 800 }*\text{ }(3)/(2000)\text{ = }(2400)/(2000)\text{ = 1.2 minutes} \end{gathered}`