Question

In 4 ​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 6 minutes. If both belts are​ used, find how long it takes to move the cans to the storage area.

Answer 1

It takes 2 minutes 4 seconds to move the cans to storage area if both the belts are used.

Explanation:

Given - In 4 ​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 6 minutes.

To find - If both belts are​ used, find how long it takes to move the cans

to the storage area.

Proof -

Given that,

Larger belt take 4 minutes to transfer the aluminium from delivery truck to storage area.

⇒ Time taken by Larger belt = 4 min/ shifting

Also,

Smaller belt take 6 minutes to transfer the aluminium from delivery truck to storage area.

⇒ Time taken by Smaller belt = 6 min/ shifting

Now,

As we know that Time is inversely proportional to time, so

Rate of Larger Belt =
`(1)/(4)` shifting/min

Rate of Smaller Belt =
`(1)/(6)` shifting/min

Now,

Let us assume that , if both belts used then,

Total time taken = x min/shifting

Then, Rate =
`(1)/(x)` shifting/min

Now,

`(1)/(4)` +
`(1)/(6)` =
`(1)/(x)`

⇒
`(6 + 4)/(24) = (1)/(x)`

⇒
`(10)/(24) = (1)/(x)`

⇒10x = 24

⇒x =
`(24)/(10)` = 2.4 minutes

∴ we get

It takes 2 minutes 4 seconds to move the cans to storage area if both the belts are used.