A conveyor belt moves 100 pounds of aluminum cans from the truck to storage in 4 minutes...

Question

A conveyor belt moves 100 pounds of aluminum cans from the truck to storage in 4 minutes. A smaller belt does the same job moving the same amount of cans in 8 minutes. How long will it take if both conveyor belts were used at the same time?

Answer 1

Kayla,

 

Let's just convert the words to math terminology:

 

Let t = time in minutes that the belts work to unload a truck of cans

Let R = rate at which the big belt unloads = 100 lbs/4 min = 25 lbs/min 

Let r = rate at which the smaller belt unloads = 100 lbs/8 min = 12.5 lbs/min 

 

Using the formula  that Pounds unloaded = (rate) multiplied by (time).  Since we have both belts operated, each contributes to the unloading, and each spends the same time unloading.  We're still unloading a total of 100 lbs.

 

Thus,  100 lbs = 25 t (by the big belt)  + 12.5 t (by the smaller belt)

Then,  100 = 37.5 t  and t = 100/37.5 = 2.667 minutes is the answer

The big belt unloads 25(2.667) = 66.7 lbs.

The smaller belt unloads 12.5(2.667) = 33.3 lbs

 

This makes sense because the big belt can do it all by itself in 4 minutes.  So with the help of the smaller belt, the original job should take less time.  In this case about 2.7 minutes.