The other answer is off.  Here's how I do it:

An accurate clock's minute hand sweeps through 24×60 = 1440 
minute marks per 24 hours.

The gaining clock's minute hand sweeps through 1440+10 = 1450 
minute marks per 24 hours.

So an accurate clock's time-lapse readings will be only 
1440/1450ths or 144/145ths of the gaining clock's time-lapse
readings.

It is a 5 hour time-lapse from 10AM to 3PM.

So the time-lapse reading of an accurate clock will be 144/145ths 
of 5 hours past 10AM.

 hours after 10AM

Then we convert  hours to minutes:



So when the gaining clock reads 3:00, the correct time will be 

2:57PM

Edwin

Already done. Duplicate of problem # 1062514.  

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