The weight W of an aluminum flatboat varies directly with the L length of the boat. If a 11-ft boat weighs 132 pounds, then what is the weight of a 13 ft boat?
I don't know what kind of a School Subject "GCU" is, but to answer your question:
Divide 132 pounds by 11 to determine the weight per foot of flatboat. Then multiply that number by 13 to determine the weight of a 13-foot boat.
156 pounds
We are given that the weight W of an aluminum flatboat varies directly with the L length of the boat. We can represent this relationship as W = kL, where k is the constant of proportionality.
To find the value of k, we can use the given information. We know that when the boat is 11 ft long, its weight is 132 pounds. So we have the equation 132 = k(11).
To find the value of k, we can rearrange the equation to solve for k: k = 132/11 = 12.
Now that we have the value of k, we can use it to find the weight of a 13 ft boat. We substitute L = 13 and k = 12 into the equation W = kL:
W = 12(13) = 156.
Therefore, the weight of a 13 ft boat is 156 pounds.
To solve this problem, we need to use the concept of direct variation. In direct variation, when two quantities are directly proportional, they can be written in the form y = kx, where y represents one quantity, x represents the other quantity, and k is a constant called the constant of variation.
In this case, the weight of the aluminum flatboat (W) is directly proportional to the length (L) of the boat. We can write this as:
W = kL
To find the value of k, we can substitute the given values into the equation. We know that when L = 11 ft, W = 132 pounds. So we have:
132 = k * 11
To find the value of k, we divide both sides of the equation by 11:
k = 132 / 11 = 12
Now that we know the value of k, we can use this to find the weight (W) of a 13 ft boat. Let's substitute L = 13 into the equation:
W = k * L
W = 12 * 13
W = 156 pounds
Therefore, the weight of a 13 ft boat is 156 pounds.