Question 1188055: Please help me solve this word question: A model steamboat is 2 ft. 3 in. long and it displaces 1.5 lb. of water. The ship of which the model is made is 720 ft. long. What is its displacement in tons?
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i believe this is a straight ratio.
the ratio is:
2 feet 3 inches divided by 1.5 pounds of water = 720 feet / x pounds of water.
2 feet 3 inches is equal to 2 + 3/12 = 2.25 feet.
the ratio becomes 2.25 / 1.5 = 720 / x
cross multiply to get:
2.25 * x = 1.5 * 720
solve for x to get:
x = 1.5 * 720 / 2.25 = 480 pounds.
there are 2000 pounds to a ton, so the displacement is 480 / 2000 = .24 tons.
Answer by ikleyn(52778)  (Show Source):
You can put this solution on YOUR website! .
A model steamboat is 2 ft. 3 in. long and it displaces 1.5 lb. of water.
The ship of which the model is made is 720 ft. long. What is its displacement in tons?
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Tutor @Theo incorrectly interprets the term " displacement " in this problem,
which leads him to crude mistake.
I came to bring you a correct solution.
Let start from the definition.
For definition of the term " displacement (for ships) " see this Wikipedia article
https://en.wikipedia.org/wiki/Displacement_(ship)
The displacement or displacement tonnage of a ship is its weight.
As the term indicates, it is measured indirectly, using Archimedes' principle,
by first calculating the volume of water displaced by the ship,
then converting that value into weight.
So, in this special problem, the term "displacement" relates to the volume of the displaced water.
The ratio of volumes of a real ship to that of a model is the cube of the similarity coefficient.
The similarity coefficient is 720 ft to 2.25 ft, i.e.  = 320.
Therefore, the displacement of the real ship is  = 49152000 lb.
You should convert this value to tons.
The term " ton " has several different meanings. But in this class of problems, it usually
denotes " long tons ", that is " a unit of weight equal to 2,240 pounds avoirdupois (1016.05 kg). (noun: long ton) "
So, we divide 49152000 lbs by 2,240 pounds and get  = 21943 tons (long tons) (rounded).
ANSWER. The ship of which the model is made has the displacement of 21943 tons (long tons).
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Solved and thoroughly explained.
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