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Question 1207330: Container A was filled with water to the brim. Then, some of the water was
poured into an empty Container B until the height of the water in both
containers was the same. Find the new height in both water containers.
Dimensions of container A: height=40, length= 25, width= 30
Dimensions of container B: height= unknown, length=25, width=18
Found 4 solutions by mananth, greenestamps, ikleyn, Edwin McCravy:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! Let x be the volume in A after pouring into B
Let y be the volume in B after pouring
Full volume in A = L*w*h =30000
x+y =30000
Volume in A after pouring
x = A*h
x = h*25*30
x = 750h
h = x/750
Volume in B = h *25*18
y = 450h
h= y/450
Heights are same after pouring
x/750 = y/450
x = y*750/450
x = 5y/3
x+y =30000 ( full volume in A)
substitute x
5y/ 3 + y = 30000
8y/3 = 30000
8y = 90000
y = 90000/8
y=11250 ( Volume in B after pouring)
x = 30000-11250
x=18750 (volume in A after pouring)
Volume / area = h
18750/750 = 25
Volume in B = 30000-18750 =11250
h= 11250/450 =25
Height same after pouring
Answer by greenestamps(13200)  (Show Source):
Answer by ikleyn(52787)  (Show Source):
Answer by Edwin McCravy(20056)  (Show Source):
You can put this solution on YOUR website!
When container A was filled with water to the brim, the volume of water in it
was lwh=(25)(30)(40).
Then, some water from A was poured into B (when B was empty), until the height
of the water in both containers was the same.
Let that common height be the unknown x.
So the height of the water in A went down from 40 to x. Therefore the volume
of water in A was reduced to lwh=(25)(30)x.
and
the height of the water in B went up from 0 to x. Therefore the volume of water
in B went up from 0 to lwh=(25)(18)x.
Then the sum of the volumes of water in both containers afterward was the same
amount of water as was in container A at the beginning, so we have an equation:
(25)(30)x + (25)(18)x = (25)(30)(40)
Solve that for x and you'll get the correct answer.
[Note. You may connect this problem to something you may have learned in your
science class as to how to get the water levels the same. Although the problem
says the water was 'poured' from A to B, a better (or at least more scientific)
way to get the levels the same would be to use a siphon. A siphon is a water-
filled tube connecting the water in the two containers. The water at the bottom
of A must support the heavy weight of all the water above it, so the upper water
in A will "push down" on the lower water in A forcing water to flow up the tube
from A into B. The heavy upper water in A will continue to "push down" on the
lower water in A, forcing water up the tube from A into B, until the water
levels are the same.]
Edwin
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