Answer: 2 pm

12 noon:    2 hours 55 minutes = 175 minutes
1 o'clock:   1 hour 15 minutes = 75 minutes
They travel 100 sign-minutes in 1 hour
So they will travel the remaining 75 sign-minutes in $\frac34$ hour = 45 minutes
They set off after lunch at 1:15 and arrive 45 minutes later at 2.