Question

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.

Answer 1

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

Answer 2

t = 3.33 minutes

Step-by-step 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
`(1)/(4)` of the task

The small conveyor takes 20 minutes to complete the task

So in one minute it completes
`(1)/(20)` of the task

When combined they will complete a certain fraction of work

Let us call it x

`X = (1)/(4) +(1)/(20) \\\\X = (6)/(20)`

Time taken to complete the task

`t = (1)/(X) \\\\t = (1)/((6)/(20) ) \\\\t = (20)/(6) \\\\t = 3.33 minutes`