SOLUTION: Two rectangular water tanks with tops on the same level are connected by a pipe through their bottoms. The base of one is 6in higher than that of the other. Their dimensions are 4

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Question 956378: Two rectangular water tanks with tops on the same level are connected by a pipe through their bottoms. The base of one is 6in higher than that of the other. Their dimensions are 4 by 5 by 2 1/2ft. and 4 by 7 by 3 ft., respectively. How deep is the water in the larger tank when the water they contain equals half their combined capacity, if the 2 1/2ft and 3ft edges are vertical?
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
Disregarding the connecting pipe:
Capacity of small tank=4ft%2A5ft%2A2.5ft=50ft%5E3
Capacity large tank=5ft%2A7ft%2A3ft=105ft%5E3
Combined capacity=50ft%5E3%2B105ft%5E3=155ft%5E3 1/2 capacity=77.5ft%5E3
If base of small tank is 0.5 ft higher:
The large tank will hold the first 6 inches: 5ft%2A7ft%2A0.5ft=17.5ft%5E3
77.5cu ft-17.5 cu ft=60 cu ft remaining to split between both tanks.
Small tank holds: (4ft*5ft*1ft)=20 cu ft per foot deep
Large tank holds: (5ft*7ft*1ft)=35 cu ft per foot deep
Combined 55 cu ft per foot deep.
60 cu ft/55cu ft/ft deep=1.09 feet deep. Each tank will add 1.09 feet of water.
The bottom 0.5 foot of the large tank is already filled, so 1.09ft+0.50 ft=1.59 ft
ANSWER 1: If the small tank is higher, there is 1.59 feet of water in the larger tank
If base of large tank is 0.5 ft higher:
The small tank will hold the first 6 inches: 4ft%2A5ft%2A0.5ft=10ft%5E3
77.5cu ft (1/2 capacity)- 10cu ft=67.5 cu ft to split between tanks.
67.5 cu ft/55 cu ft=1.23 feet deep. Each tank will add 1.23 feet of water
ANSWER 2: If the large tank is higher, there is 1.23 feet of water in the larger tank.