In 4 minutes, a conveyor belt moves 300 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 20 minutes. if both belts are used, find how long it takes to move the cans to the storage area.

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lilaipo lilaipo · Answer 1 · 2018-05-22T14:04:06+02:00

The answer is 1.5 minutes

let t = time required when both belts are used

Let the completed job = 1 (moving 300 lb)

1/2+1/6=1

Multiply by 6
6*t/2 + 6*t/6 = 6
6t/2+6t/6=6
3t + 1t = 6
4t = 6
t = 6/4

t = 1.5 min

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Chlidonias Chlidonias · Answer 2 · 2019-09-29T10:11:40+02:00

Answer:

t = 3.33 minutes

Explanation:

We need to move 300 pounds of material

The large conveyor takes 4 minutes to complete the task.

So we can say in one minute it will complete [tex]\frac{1}{4}[/tex] of the task

The small conveyor takes 20 minutes to complete the task

So in one minute it completes [tex]\frac{1}{20}[/tex] of the task

When combined they will complete a certain fraction of work

Let us call it x

[tex]X = \frac{1}{4} +\frac{1}{20} \\\\X = \frac{6}{20}[/tex]

Time taken to complete the task

[tex]t = \frac{1}{X} \\\\t = \frac{1}{\frac{6}{20} } \\\\t = \frac{20}{6} \\\\t = 3.33 minutes[/tex]