outty wrote:Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute, and gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P?
6
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One approach is to use equivalent ratios.
We know that, for every
60 seconds, Q makes
30 more revolutions than P does.
We want to determine
how many seconds it will take Q to make
6 more revolutions than P does.
We may immediately see that it will take 1/5 the time (i.e.,
12 seconds), but let's use equivalent ratios.
The ratio will be: (
# of seconds)/(
# of extra revolutions Q makes).
So, we get:
60/
30 =
x/
6
Cross multiply to get 30x = (60)(6)
x =
12
In other words, it will take
12 seconds.
Cheers,
Brent
