WholeLottaLove 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 makes in terms of x ?
The larger rim must circulate for the same number of inches the smaller rim does.
C = (pi)d
C(small): (pi)*28
C(large): (pi)*35
Lets say the time horizon is 60 seconds, so during that time the smaller rim covers a distance of (pi)*28*60 = (pi)*(1680) inches
(pi)*(1680) = (pi)*(35)(x)
pi*(48) = pi*(x)
48=x
Answer: C. 48x
I'm wondering if someone can help me with my equation here. I got it mostly correct, however, my final answer of x=48 wasn't quite the answer that is correct (48x) so I got a bit lucky in choosing it. I first multiplied the small rim by 60 seconds to get it in terms of one minute. I then set it equal to the circumference of the larger rim which I multiplied x to get the number of revolutions it would make so that distance covered by the two rims was the same. Can someone explain to me why this is not entirely correct?
Thanks!!![:-D]( "Very Happy")
Here is my reasoning behind this question...I am not sure if it is correct or not but here it goes: The smaller rim rotates the same distance as the larger rim. This means that for a given time, the larger wheel rotates less. 28(pi) represents the smaller wheel and 28(pi)*(x) represents the number of revolutions it makes. 60*28*(pi)*x converts it into minutes (60 seconds/1 minute) as the question asks. On the other side of the equal sign is 35(pi). We are looking for the number of revolutions 35(pi) makes which we know to be a different number than the revolutions the smaller wheel makes, so we set it to n: 35(pi)*n. We are looking for the answer in terms of x so we should cancel out as much as possible while leaving x in the answer. Therefore, the final equation is 1680*(pi)*x = 35*(pi)*n ==> 48*(pi)*x = (pi)*n ==> 48x = n. Does that sound right?
The larger rim must circulate for the same number of inches the smaller rim does.
C = (pi)d
C(small): (pi)*28
C(large): (pi)*35
Lets say the time horizon is 60 seconds, so during that time the smaller rim covers a distance of (pi)*28*60 = (pi)*(1680) inches
(pi)*(1680) = (pi)*(35)(x)
pi*(48) = pi*(x)
48=x
Answer: C. 48x
I'm wondering if someone can help me with my equation here. I got it mostly correct, however, my final answer of x=48 wasn't quite the answer that is correct (48x) so I got a bit lucky in choosing it. I first multiplied the small rim by 60 seconds to get it in terms of one minute. I then set it equal to the circumference of the larger rim which I multiplied x to get the number of revolutions it would make so that distance covered by the two rims was the same. Can someone explain to me why this is not entirely correct?
Thanks!!
Here is my reasoning behind this question...I am not sure if it is correct or not but here it goes: The smaller rim rotates the same distance as the larger rim. This means that for a given time, the larger wheel rotates less. 28(pi) represents the smaller wheel and 28(pi)*(x) represents the number of revolutions it makes. 60*28*(pi)*x converts it into minutes (60 seconds/1 minute) as the question asks. On the other side of the equal sign is 35(pi). We are looking for the number of revolutions 35(pi) makes which we know to be a different number than the revolutions the smaller wheel makes, so we set it to n: 35(pi)*n. We are looking for the answer in terms of x so we should cancel out as much as possible while leaving x in the answer. Therefore, the final equation is 1680*(pi)*x = 35*(pi)*n ==> 48*(pi)*x = (pi)*n ==> 48x = n. Does that sound right?