Math
posted by Anonymous on .
A wire that weighs 9 ounces per meter is stretched from point D to point B. Another wire is stretched from point B to point A that weighs 8 ounces per meter. If you know the total weight of the two wires is 197 ounces, how far is it from point B to C?
*On my homework, there is a drawing of the wires... It makes sort of like a triangle flag shape.. It is a right triangle. We don't know the BASE of that triangle, which is the distance from point B to C, B being the bottom point and C being the top. So the triangle is a right triangle with the base on the left.. From Point B, there is a wire going down to point A.. The distance from Point C to Point A is 15 meters. The top of the triangle is point D. The leg of the triangle, which is the distance from Point D to C is 12 meters... If you need more information just ask..

First you need to determine all of the different segments in terms of x. You have:
AB=Unknown
BC=Unknown
CD=12m
BD=Unknown
All of the Unknown's will be in terms of some X value. For simplicity's sake let's say BC=x (ultimately this is what you want to solve for you can do it the other way and make AB=x). We also know that AC=15m and AB+BC=AC so we can determine AB and BC. So now you have:
AB=15x
BC=x
CD=12
BD=Unknown
BD is the hypotenuse of a right triangle with BC and CD it's sides. So using the Pythagorean Theorem you can solve for BD in terms of x to get the following:
AB=15x
BC=x
CD=12
BD=squareroot(x^2+144) or (x^2+144)^(1/2)
Now the important part is to notice the units. BD is 9oz/m and AB is 8oz/m. The total weight however is only 197oz. Not oz/m. So you need to multiply the segment length by it's weight/length in order to determine it's actual weight. Then we know that these two weights equal 197 oz. So your equation will look like this:
8*AB+9*BD=197
So,
8*(15x)+9*(x^2+144)^(1/2)=197
At this point you can solve for x, which as we originally defined it is the BC length.
You get: x=5 or x=67.47
This is a real world problem, and the entire wire of AC is 15m. So you can't have a segment of it be 67.47m. Therefore the only possible answer is 5m.
P.S. If one value is negative then you have the same issue. There aren't any negative lengths. So only one value will work.