Math Problem Challenge: Two Wheels?

Question

*Two Wheels*

One wheel turns at 33 1/3 revolutions per minute. A second wheel turns at 45 revolutions per minute. At some point in time, a mark on each wheel is at the lowest point on each wheel at the same time. What is the least number of seconds until the marks on both wheels are again both at the lowest point at the same time?

Justify your answer and show all work!

This is a problem challenge for school and it is very confusing. i have ideas of how to solve it but i'm not sure how to go about it. This is for extra credit and due tomorrow, 10/24/07, so please try and solve this as soon as you can. Thank You!!!

Answer 1

36 seconds

It takes the first wheel 1/(33 + 1/3) or 3/100 of a minute to make one revolution. It takes the second wheel 1/45 of a minute to make one revolution. Finding a common denominator for these fractions, we see that the first wheel takes 27/900 of a minute to make one revolution, and the second wheel 20/900 of a minute. Now, 27 and 20 have no prime factors in common, so their least common multiple is just 27*20 = 540. Therefore, the next time the marks on both wheels are at the lowest point will be at 540/900 of a minute, which is 54/90 = 27/45 = 3/5 of a minute, of 36 seconds.