Twelve soldiers had to get to a place twenty miles distant as quickly as possible and each had to arrive at the same time. They requisitioned the services of a man with a small car.
“Through this zone I can do a constant 20 miles an hour, but I cannot carry more than four men at a time. At what rate can you walk?”
“All of us can do a steady four miles an hour.”
“Very well, then I will go ahead with four men, drop them somewhere on the road to walk, then will pick up four more (who will already have started out), drop them also, and return for the last four. So all you have to do is keep walking while you are on your feet and I will do the rest.”
They started at noon and arrived safely, together, at the same time, according to plan.
What was the exact time they arrived?
If you follow your intuition that the first group rides then walks the remainder and the second goes walk, ride, walk and the third goes walk ride, then each of these distances can be related.
d1 = distance first group rides
d2 = distance first group walks = 100-(23/3)*d1
d3 = distance 2nd group walks 1st time = d1/3
d4 = distance 2nd group rides = d1
d5 = distance 2nd group walks 2nd time = 20-(4/3)*d1
d6 = distance 3rd group walks = (2/3)*d1
d7 = distance 3rd group rides = 100-(22/3)*d1
Total distance of 20 ->
group 1: ride(12), walk(8)
group 2: walk(4), ride(12), walk(4)
group 3: walk(8), ride(12)
Total time = 12/20 + 8/4 = 2.6 hours
They all arrive at 2:36pm
doing some math
