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two leaky containers are filling with water. water enters container a at a rate of 2/3 cup per 1/2 minute and leaks out at a rate of 1/4 cup per 3/4 minute. water enters container b at a rate of 3/4 cup per 1/2 minute and leaks out at a rate of 1/2 cup per 3/4 minute. which container needs to be filled faster in order for both containers to gain the same amount of water per minute? by how much more water per minute? explain

User Cursa
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container B needs to be filled faster in order for both containers to gain the same amount of water per minute , and by 1/6 water per minute .

Explanation:

Here we have , two leaky containers are filling with water. water enters container a at a rate of 2/3 cup per 1/2 minute and leaks out at a rate of 1/4 cup per 3/4 minute. water enters container b at a rate of 3/4 cup per 1/2 minute and leaks out at a rate of 1/2 cup per 3/4 minute. We need to find which container needs to be filled faster in order for both containers to gain the same amount of water per minute . Let's find out:

Rate of Filling container A:


((2)/(3) )/((1)/(2) )


(2)/(3) (2) = (4)/(3)

Rate of leaking Container A:


((1)/(4) )/((3)/(4) )


(1)/(4) ((4)/(3)) = (1)/(3)

Amount of water in Container A in one minute :


(4)/(3) - (1)/(3) = 1

No , following same for Container B

Rate of Filling container B:


((3)/(4) )/((1)/(2) )


(3)/(4) ((2)/(1)) = (3)/(2)

Rate of leaking Container B:


((1)/(2) )/((3)/(4) )


(1)/(2) ((4)/(3)) = (2)/(3)

Amount of water in Container B in one minute :


(3)/(2) - (2)/(3) = (5)/(6)

Since , Rate of water per minute in container A is 1 and , Rate of water per minute in container B is 5/6 , container A fills faster by container B by


1-(5)/(6) = (1)/(6)

Therefore , container B needs to be filled faster in order for both containers to gain the same amount of water per minute , and by 1/6 water per minute .

User MrNetherlands
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