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;

$\frac{800\text{ lbs}}{3\text{ minutes }}\text{ = }\frac{800}{3}\text{ lbs/min}$

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;

$\begin{gathered} \frac{800}{400+\frac{800}{3}} \\ =\text{ }\frac{800}{\frac{1200+800}{3}} \\ \\ =\text{ }\frac{800}{\frac{2000}{3}} \\ =\text{ 800 }\times\text{ }\frac{3}{2000}\text{ = }\frac{2400}{2000}\text{ = 1.2 minutes} \end{gathered}$