Hi!
You can solve this doing a lot of math, but any time you have variables in the choices, you can also pick numbers to solve - and picking numbers is often much easier than algebra. Let's try it a couple of different ways!
Before we jump in, let's make sure we identify exactly what the question is asking - we want the number of revolutions per
minute of the larger rim. Since all of the other information is in seconds, we'll have to remember to convert units at the end.
To go from diameter to circumference you simply multiply by pi; since both rims will have pi in the circumference, we can safely ignore it (the pis will all cancel out).
If we proceed by picking numbers, we want to pick a distance that's divisible by both 28 and 35 (to keep the math simple). Since 28 and 35 have "7" in common, we can either multiply 28 by 5 (since 35=7*5) or 35 by 4 (since 28=7*4) to get our lowest common multiple. Either way, our LCM is 140.
So, let's let the distance travelled be 140 inches. The smaller rim makes 140/28=5 rotations and the larger one makes 140/35=4 rotations. Accordingly, x=5 and, in terms of x, the larger rim makes 4/5(x) rotations per second.
To convert from rps to rpm, we have to multiply by 60, giving us the final answer of:
(4/5)(60)x = 48x... choose C!
We can also solve this problem fairly quickly using ratios.
Since both rims travel the same number of inches/second, the number of revolutions travelled will be inversely proportional to the relative sizes of the rims. Since the bigger rim is 5/4 the size of the smaller one, it will make 4/5 the number of rotations.
Now we have to remember to convert rps to rpm; multiplying by 60 will once again lead to choice (C).
grandh01 wrote:A circular rim 28 inches in diameter
rotates the same number of inches per
second as a circular rim 35 inches in
diameter. If the smaller rim makes x
revolutions per second, how many
revolutions per minute does the larger
rim make in terms of x?
(A)48Ï€/x
(B) 75x
(C) 48x
(D) 24x
(E) x/75
OA is C
