Re: Puzzler of the week

[David L. Gomez]

My Answer:   Let "T" represent the amount of time it takes for Throckie to make six jumps (covering a distance of 60 inches), or for Rocky to make ten jumps (also covering a distance of 60 inches).   Therefore, Throckie has a jump rate of 6 Jumps per Time "T", while Rocky has a jump rate of 10 Jumps per time "T".   The race covers a distance of 144" out, and 144" back.   If Throckie makes a series of 14 jumps, he will cover a distance of 140 inches, so he will have to make a 15th jump to cover the 144" (even though in doing so he overshoots the required distance by 6"). Therefore, he will have travelled a distance 150" out from the START/FINISH line. He will then have to make 15 full jumps to make it back to the START/FINISH line. With a jump rate of 6 Jumps per T, it will take him a total time of (15+15)/6 = 5T to complete the race.   Meanwhile, if Rocky makes a series of 24 jumps, he will cover a distance of 144", so he would need to turn around and make another 24 jumps to make it back to the START/FINISH line. With a jump rate of 10 jumps per T, it will take him a total time of (24+24)/10 = 4.8T to complete the race.   Since 4.8T is less than 5T, Rocky would be the WINNER of the race.   Dave ----- Original Message ----- From: Scott MacLean To: MacLean List ; Georgetown Crew Mailing List Sent: Thursday, August 29, 2002 11:30 PM Subject: Puzzler of the week This week's puzzler: Two grasshoppers are hanging around, and each is boasting that he is faster than the other. To settle the argument, they decide to have a race. The larger of the grasshoppers, Throckmorton -- or Throckie, as he's known -- can jump 10 inches at a single bound. The other grasshopper, Rocky, can jump only six inches at a shot. So the larger grasshopper says, "We're going to set up a racecourse that's 24 feet long: 12 feet out and 12 feet back." They're each at the starting point. Vinnie Goombatz-Hopper shoots the gun, and they take off. Now, even though Throckie is the bigger guy and can jump 10 inches at a shot, Rocky jumps more often. So when they get to the five-foot mark -- which is 60 inches -- the big guy has jumped six times and the little guy has jumped 10 times, but they're dead even...neck and neck...antennae to antennae. The question is: Which one wins the race, and why?