# Find the formula

10 feet of common 2-inch-bore lead piping weighs 50 lb. What is the formula for the weight of x feet of such lead piping? --Sawyer, Mathematician's Delight

I am not sure about what I am asked to do here. It is known that $$10F*2=50$$ and I am asked to write it down as $$XF*2=W$$ or is it something else?

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## 2 Answers

Let $W$ be the weight as a function of the length $L$. So you know that when $L= 10$ ft then $W = 50$ lb. We sometimes will write this as $W(10) = 50$.

Now if $10$ ft weighs $50$ lb, then what would $5$ ft weigh? Well, half of that, i.e. $25$ lb. What would $1$ foot weigh? Well, one tenth of that, i.e. $5$ lb.

So $1$ foot of pipe weighs $5$ lb. $2$ ft would weight the double of that. Can you find the formula now? (Note that the fact that the pipe is $2$ in thick doesn't matter.)

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First of all, the 2 in the "2-inch-bore" is utterly irrelevant and has no place in any formula. Think of it as "10 feet of (whatever-you-want) weighs 50 pounds: $x$ feet weighs how many pounds?" You want a formula for "how many", and you want that formula to involve $x$.

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