Yalephd wrote:

Circular gears L and R start to rotate at the same time at the same rate. Gear L makes 10 complete revolutions per minute and gear R makes 40 revolutions per minute. How many seconds after the gears start to rotate will gear R have made exactly 6 more revolutions than gear L?

a) 6

b) 8

c) 10

d) 12

e) 15

As we can see, Gear R makes 30 more revolutions per minute than Gear L does. So, we can set up the following proportion to solve for the number of seconds for Gear R to make 6 more revolutions than Gear L does:

30 revolutions/1 minute = 6 revolutions/x seconds

We need for both denominators to have the same units. Since 1 minute = 60 seconds, we can re-express the proportion as:

30/60 = 6/x

Cross multiplying, we have:

30x = 360

x = 12

Alternate Solution:

Gear L makes one revolution in 60/10 = 6 seconds and gear R makes one revolution in 60/40 = 1.5 seconds. If we let n the time (in seconds) that passes when gear R makes 6 more revolutions than gear L, we can create the following equation:

n/1.5 - n/6 = 6

Let’s multiply each side by 6:

4n - n = 36

3n = 36

n = 12

Answer: D

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