Solve math problem. Show work.?

Question

One wheel turns 33 1/3 revolutions per minute. A second wheel turns at 45 revolutions per minute. At some point,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 at the lowest point at the same time?

Answer 1

First wheel rotates with a time period of 60 x 3 / 100 = 1.8 seconds = 9/5 seconds

Second wheel rotates with a time period of 60 / 45 = 1 1/3 seconds = 4/3 seconds

We need a time T, so that

1.8 n = T = 1.3333 m where both m and n are integers

So, we write out the multiples of 1.8 and 1 1/3 and see where they join or we can do it graphically.

1.8, 3.6, 5.4, 7.2, 9.0, 10.8, 12.6, 14.4, 16.2, 18, 19.8, 21.6,

1.333, 2.666, 4, 5.333, 6.666, 8, 9.333, 10.666, 12, 13.333, 14.666, 16, 17.333, 18.666, 20, .......

You need to work out where the number becomes common. Graphical solution is easier.

Answer 2

3 secs

they got to meet when both the no of revolutions made is a whole number at that second. hence 3 secs