Traveling in the direction of Hogwarts at a constant speed for the entire trip, Larry was one-eighth of the way to Hogwarts at 5:00 a.m. At 8:00 a.m. on the same day he was three-fourths of the way to Hogwarts. Knowing Larry's starting location and Hogwarts are in the same time zone, what time did Larry arrive at Hogwarts?

Question

anonymous · Answer

r t = d, r = d/t

Let t be the elapsed time Larry took to travel from the starting point to 1/8 of the way to Hogwarts.

At the 3/4 point, where 75% of the trip distance was completed, Harry had taken t+3 hours from the starting point.  The problem statement says that the rate, or speed, was constant the entire trip, therefore, the speed for the 1/8th leg can be equated to the speed for the 3/4 leg.

Solve the following for t where t is the elapsed time in minutes, not hours:$$\frac{1/8}{t}= \frac{3/4}{t+(3*60)}$$$$t=36 \text{ minutes}$$At 0500 Harry had 7/8 of the trip to complete.  If it takes 36 minutes to complete 1/8th of the trip, then it takes 7*36 or 252 minutes or 4hrs and 12 minutes past 0500 to complete the trip.

Harry rolled into Howgwarts at 0912 military time or 9:12AM.