April ACT Math - Pulley Question

<p>Can someone please explain how I should solve this problem? If you can't remember the numbers, just make it up. Thanks!</p>

<p>I remember the problem entirely with every unit, and could explain how to solve it, but it would take far too long to explain. Even with pen and paper and knowing exactly what to do beforehand, it would take >5 minutes to explain. If you ask me or anyone else I know, they all agree the question did not belong on the ACT. I have no idea what they were thinking putting the question on the test. It is physically not possible to solve in a reasonable amount of time (I asked multiple people with 36’s on math, who are in AP Calc BC and beyond and no one could solve it in under 10 minutes). By making fairly accurate assumptions the problem can be solved in 1-2 minutes, but I don’t see why the ACT wants us to make assumptions on this problem, when they don’t for any others. </p>

<p>I’m not complaining, since I got the question correct. I’m just giving my opinion, that it should not have been on the ACT. </p>

<p>I’ll attempt to. I didn’t think it was really that hard, but this might be hard to explain.

  1. Calculate the length of the pulley sections that went around the circles. You can do this by finding the circumference of each circle and then multiplying it by 2/3 or 1/2 or how much the problem said it wrapped around.
  2. Find the length of the pulley sections in between. You already eliminated three answers from step 1, so you were left with blah blah + 8 or blah blah +8rad3 . Drawing a reasonable inference from the appearance of the circles would leave you with a 30-60-90 triangle. This is hard to explain but all the angles follow a pattern.
  3. Making a reasonable guess at this point, rather than taking the time to find it out, you realize that a 30-60-90 triangle’s pattern has something to do with rad3, so you wisely guess blah blah + 8rad3 and get the question right in under a minute.
    Hope that helped! If not, feel free to message me. </p>

<p>Uggh I still have no idea how to do this question. I ended up guessing correctly, but it is bothering me. The Math Section is usually pretty straightforward for me, but that questioned definitely flustered me a little lol. How in the world do you get the length of the 2 parts of the pulley that aren’t part of the circumference of either circle? I don’t remember being able to form any right triangles… I just guessed 8rad3 (~14) because each part of the pulley seemed closer in length to 7 than 4. It never said figures were NOT to scale…</p>

<p>@collegeman5 Don’t worry about it, you guessed right. The angles in the triangles formed by the diameters and the pulley line made a 30-60-90 triangle which means it was whatever + 8rad3</p>