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.

Question

02-07-2017
Mathematics

contestada

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.

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laysysla laysysla · Answer 1 · 2017-07-02T22:39:34+02:00

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

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.

Respuesta :

Otras preguntas

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.