The weight W of an aluminum flatboat varies directly with the length L of the boat. If a 7-foot boat weighs 105 pounds, then what is the weight of a 14-foot boat?
W = kL
That is, W/L is constant. So, you want W such that
W/14 = 105/7
To find the weight of a 14-foot boat, we first need to understand how the weight and length are related. The problem states that the weight of an aluminum flatboat varies directly with the length of the boat. This means that if we double the length of the boat, the weight will also double.
We are given that a 7-foot boat weighs 105 pounds. To find the weight of a 14-foot boat, we can set up a proportion:
Weight of 7-foot boat / Length of 7-foot boat = Weight of 14-foot boat / Length of 14-foot boat
Using the given information, we have:
105 pounds / 7 feet = Weight of 14-foot boat / 14 feet
To solve for the weight of the 14-foot boat, we can cross-multiply:
105 pounds * 14 feet = Weight of 14-foot boat * 7 feet
1470 pounds = Weight of 14-foot boat * 7 feet
Now, we can isolate the weight of the 14-foot boat by dividing both sides of the equation by 7 feet:
Weight of 14-foot boat = 1470 pounds / 7 feet
Simplifying the right side of the equation, we get:
Weight of 14-foot boat = 210 pounds
Therefore, the weight of a 14-foot boat is 210 pounds.