Problema Solution
Luke and Slim have only one horse. Luke rides for an agreed upon distance and then ties up the horse for Slim, who has been walking. Meanwhile, Luke walks ahead. The two men alternate walking and riding. If they walk 4mph and ride 12mph, what is each man's average speed? What fraction of the time is each man riding? What fraction of the time is the horse resting?
Answer provided by our tutors
For all distances, it takes the walker three times as long to cross the same distance as the rider.
In one hypothetical, let us imagine the agreed upon distance for riding is 12 miles. This would mean that the rider rides for exactly 1 hour, ties up the horse, then begins to walk.
Hour 1: Luke rides 12 miles, Slim walks 4 miles. Slim is 8 miles away from the horse. They are now both walking.
Hour 2: Luke walks 4 miles (now 16 miles from the starting spot), Slim walks 4 miles (8 miles from start, 4 miles until the horse).
Hour 3: Luke walks 4 miles (now 20 miles from the starting spot), Slim walks 4 miles and reaches the horse (12 miles away from start).
Hour 4: Luke walks 4 miles (now 24 miles from the starting spot), Slim rides 12 miles (now 24 miles from the starting spot).
At the end of hour 4, bgoth Luke and Slim are 24 miles away from the starting spot and switch ridership of the horse, beginning the cycle anew. In this time, each of them has walked for 3 hours and ridden for 1. The horse stood idle for 2 of those hours. Each man crossed 24miles in 4 hours, resulting in an 8mph average speed (24m/4h = 8 m/h).
Therefore each man's average speed is 8mph, each man spends 1/4th of the time riding, and the horse is resting 1/2 of the time.