# Rocky vs. Throckie

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.”

So they take off.

Now, even though Throckie, the bigger guy, can jump 10 inches at a shot, the little guy, 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?

### 2 guesses to Rocky vs. Throckie

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• RiddleCracker

Im thinking that sense Rocky jumps more often he will get tired and slow down allowing Throckie to win!

• Nanao Ise

Yay, mathematics!

â€¦Well, the way this is put, the grasshoppers are tied every five feet assuming they don’t tire or anything like that during the race. The “race”, then, would be those last four feet.

I’m just going to say that it takes them a minute to go five feet, for a steady time reference. So Rocky’s jumping every six-second interval, while Throcky is jumping every ten.

And – doing a bit of an oddball step, here, but it works – that means that Rocky reaches the finish line in eight jumps, or in 48 seconds.

Throcky will reach the finish line in five jumps, or in 50 seconds – because doing it with four would put him eight feet before the finish line.

Rocky comes in first by two seconds’ time.