This clock was set right at the time shown, 7 in the morning. It loses 4 minutes every hour. When it shows 1:00 p.m., what is the correct time?

The dial has moved 6 h = 360 min, but it moves only 56 min per true hour. True time passed $=360\times \frac{60}{56}=385\frac{5}{7}$ min = 6 h $25\frac{5}{7}$ min, so it is $25\frac{5}{7}$ min past 1. (24 min adds 4 min for each of 6 hours.)