Question 1114309
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<U>Answer</U>.  Faster gear makes 4 revolutions per minute, while the slower gear makes 3 revolutions per minute.


<U>Check</U>.  The faster gear makes one revolution in 60/4 = 15 seconds.

        The slower gear makes one revolution in 60/3 = 20 seconds.


        Difference of times to make 1/5 revolution is  (20-15)/5 = 1 second.
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<U>Solution</U>


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Let n be the number of rotations of the faster gear per minute.

Then the number of rotations of the slower gear per minute is (n-1),  according to the condition.


The time to make one rotation for faster gear is  {{{1/n}}}  of an minute for the faster gear  and  {{{1/(n-1)}}}  of an minute for the slower gear.


The difference  {{{1/(n-1)}}} - {{{1/n}}}  is equal to 5 seconds,  or  {{{5/60}}}  of the minute,  according to the condition.


So, the equation is


{{{1/(n-1)}}} - {{{1/n}}} = {{{5/60}}},


and when you solve it, you will get the answer claimed above.
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