Ridiculous riddle un-rigourous!
December 9 2019
It’s clever to pace the travellers so their time on the hill has the same average speed for the duration as their flat travel. They are twice as fast coming down in half the time as going up so the average over time is ( 2t x 3kph + 1t x 6kph )/3t= 4kph, it does not change with time t. Time of travel is 6 hours so total distance is 6x4kph = 24 miles. It doesn’t matter how far the top of the hill is so long as they get there in 3 to 4 hours. If there was no hill they get to the middle in 3 hrs, 3hrs back. If it was all hill they get to the top in 4 hrs and turn around to get back in two hours. Or anywhere in between. So what? If you have any maths skills and are trusting you assume the riddle has a solution solvable by simultaneous equations and spend half your morning trying to write them before resorting to graphing it. Time on the horizontal and distance away from start on the vertical. If you shift the steep all hill triangle to the left it intersects the no hill triangle at the same distance from start on both sides.
Phooey on unsolvable riddles!