Question

In 5 minutes, a conveyor belt moves 100 pounds of recyclable aluminum from the delivery truck to a storage area. A smaller belt moves the same quantity of cans thesame distance in 9 minutes. If both belts are used, find how long it takes to move the cans to the storage area.The conveyor belts can move the 100 pounds of recyclable aluminum from the delivery truck to a storage area in minutes.(Simplify your answer. Type an integer, fraction, or a mixed number.)

Answer 1

we know that

a greater conveyor belt moves 100 pounds ------------> 5 minutes

so

Applying proportion

1-minute ---------> move 100/5=20 pounds

a smaller conveyor belt moves 100 pounds ------> 9 minutes

so

Applying proportion

1-minute --------> move 100/9 pounds

therefore

If both belts are used

then

1-minute --------> move 20+(100/9)=(180+100)/9=280/9 pounds

Applying proportion

Find out how long it takes to move 100 pounds

$\begin{gathered} \frac{1}{\frac{280}{9}}=\frac{x}{100} \\ \\ solve\text{ for x} \\ x=\frac{100}{\frac{280}{9}}=\frac{900}{280} \end{gathered}$

Simplify the fraction

45/14

Convert to a mixed number

45/14=42/14+3/14=3 3/14 minutes

The answer is 3 3/14 minutes