Byron S. answered • 10/07/14
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The question indicated two properties of the carts that you're interested in, weight and capacity. Each one will give an equation that will help solve the problem.
Let w be the number of wooden carts, and m be the number of metal carts.
The total weight is 10,000 tons, each wooden cart weighs 1 ton, and each metal cart weighs 25 tons.
(1 ton)w + (25 tons)m = 10,000 tons
The total capacity needs to be 100,000 m3, each wooden cart holds 300 m3 and each metal cart holds 80 m3.
(300 m3)w + (80 m3)m = 100,000 m3
Now with two equations and two unknowns, you can solve!
Please comment if you have more questions.
Byron S.
The solution you get from these equations will give you the minimum number. Since there is no limit given on the the number of cars, you could replace a single metal car with 25 wooden cars for the same weight, but considerably more carrying capacity (80 m3 vs 25*300 = 7,500 m3).
At one extreme, for 10,000 tons you could have 10,000 wooden carts on the train, for a total carrying capacity of 3,000,000 m3.
On the other hand, to carry 100,000 m3 of cargo, you could use 100,000/300 = 333.33 = 334 wooden carts to carry the required cargo, but then your train only weighs 334 tons. Roughly every 4 metal carts can carry the same amount as 1 wooden cart, but increases the weight (which in this case is a good thing.) When you solve the equations above, you'll find out how many less than the 334 you actually need, when replacing some of the wooden carts with metal carts.
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10/07/14
Byron S.
The answer to these equations is the minimum. You could, in theory, replace any of the metal carts with 25 wooden carts to weigh the same amount, but increase your carrying capacity by quite a bit.
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10/07/14
Jason K.
Ah, that's it. I was looking for a formula, when I needed a loop function. Thanks.
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10/07/14
Jason K.
10/07/14