The strength of a wood beam varies inversely with its length. A beam is 33 feet long can support 1200 pounds. How much weight can a similar beam support if it is 23 feet long?
To solve this problem, we can use the inverse variation formula:
Strength1 * Length1 = Strength2 * Length2
From the information given, we know that:
Length1 = 33 feet
Strength1 = 1200 pounds
Let's substitute these values into the formula:
1200 * 33 = Strength2 * 23
Now, we can solve for Strength2:
39600 = Strength2 * 23
To find the value of Strength2, we divide both sides of the equation by 23:
Strength2 = 39600 / 23
Calculating this value:
Strength2 ≈ 1721.74 pounds
Therefore, a similar beam that is 23 feet long can support approximately 1721.74 pounds.
To solve this problem, we need to understand the concept of inverse variation. Inverse variation, also known as inverse proportion, occurs when one variable increases while the other variable decreases, and they are related by the equation y = k/x, where y is the dependent variable, x is the independent variable, and k is the constant of variation.
In this case, the strength of the wood beam is the dependent variable (y), and the length of the beam is the independent variable (x). According to the question, the strength of the beam varies inversely with its length. So we can write the equation as: strength = k/length.
We are given that the beam is 33 feet long and can support 1200 pounds. Let's substitute these values into our equation to find the value of k:
1200 = k/33
To solve for k, we can cross multiply:
1200 * 33 = k
k = 39600
Now we have the value of k. We can use it to find the weight that a similar beam can support if it is 23 feet long. Let's set up the equation:
strength = k/length
strength = 39600/23
Now we can calculate the strength of the similar beam:
strength = 1721.73913 pounds (rounded to the nearest pound)
Therefore, the weight a similar beam, which is 23 feet long, can support is approximately 1721 pounds.
stength = k(1/length)
if length = 33, then strength = 1200
1200 = k/33
k = 39600
so : strength = 39600/length
if length = 23
strength = 39600/23 = 1721.7