Rate of time gain on a "fast" clock

A “fast” clock gains time at the same rate every hour.  It is set to the correct time at 10 a.m. When the fast clock shows 11 a.m. the same day, the correct time is 10:52 a.m. When the fast clock shows 3:30 p.m. that day, what is the correct time?

MetroEye: fast clock gains time at the same rate every hour. 

Number of hours between 10 a.m. and 3.30 p.m. = 5.5 hours
From 10 a.m. to 11 a.m. clock gained 8 minutes => Rate of gain = 8 min/hour

The time gained when the fast clock shows 3.30 p.m. = 5.5 hours * 8 min/hour = 44 mins

The correct time when the fast clock shows 3.30 p.m. = 3.30 p.m. - 44 mins = 2.46 p.m.

So the correct time is 2.46 p.m.