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.
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
