Rope Problem – Graphic Solution Path

Hi guys! Today we’re going to look at the rope problem. And this is a fairly straight forward problem with an excellent graphic solution path. But there are some obstacles in our way to that graphic solution path.

Obstacles To Avoid

The first thing to watch out for here is the phrasing of the problem. You’ll notice it is phrased in an awkward way: rather than telling us where the rope is cut, it tells us one length relative to the other. The other obstacle is that we immediately want to jump into the math. Either setting up an algebraic equation or, otherwise, not visualizing the rope.

And this is an error not because it’s that much more difficult to do it mathematically, but because it’ll take you a bit more time and it will be less clear. You won’t be as confident in your answer choice relative to actually being able to see it.

Visualize the Problem

So, what you want to do is visualize the actual rope. And we’ve got one right here. So, if this is 40 feet long, and one side is 18 feet longer than the other then we wanna take the 18 and make that the longer piece, and then the other two pieces are distributed among the short side and the rest of the long side. Once we have that we can say, well, if this long part here is 18, then these two pieces must be 22 they also must be equal. And this is much quicker and clearer than setting up an equation 2x+18 = 40

We’re doing the same thing but here it’s easy to say: okay, 11; 11+18 is 29, that gets us our 40. And we’re there, we’re confident, we move on.

This is a great example of a straightforward problem that can be done in 15 seconds and if you’re doing it in a minute you’re spending too much time. Hope this helps, and we’ll see you guys next time!

For other problem related to this, try out the Test Averages Problem.

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