Problem:

Driver starts out in the morning on a drive and leaves exactly on the minute. After going 10 miles, she looks down at her watch and notes that the hour and minute hands coincide – both pointing in same direction. She traveled the 10 miles at an average velocity of 44 mph. What time did she leave on her drive?

At a speed of 44 MPH, the 10 mile point was reached in 7 min and 20 seconds. There are 11 times in the AM when the watch hands will coincide. I can calculate from any hour the point between that hour and the next (~65 min interval) when the hands will align. So it seems to me that the departure time could be within any of these intervals by finding the hands align time and back up 7min, 20 sec. I don’t see how you arrive at a precise departure time. Am I correct in this assumption, and could this situation be expressed algebraically?