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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