Question

In 3 ​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 24 minutes. If both belts are​ used, find how long it takes to move the cans to the storage area.

Answer 1

You need to add their rates of working
to get their rate working together
For the bigger belt:
Rate1 = (300 pounds of aluminum) / (3 minutes)
For the smaller belt:
Rate2 = (300 pounds of aluminum) / (7 minutes)
I will call moving 300 pounds of aluminum 1 job
So, Rate1 =  1/3
and Rate2 =  1/7 

Let t = time in minutes for both belts to do this job
Rate 1 + rate2 = Rate3
1/3 +1/7+1/t

Multiply both sides by 21t
7t+3t=21
10t=21

 t=2.1 min
Note that .1  min = 6 sec
Working togethers, the belts can move the cans
in 2 min and 6 sec