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Taking that internship in a remote mountain lab might not have been the best idea. Pulling that lever with the skull symbol just to see what it did probably wasn’t so smart either. But now is not the time for regrets because you need to get away from these mutant zombies…fast. Can you use math to get you and your friends over the bridge before the zombies arrive? Alex Gendler shows how.
Answer: At first it might seem like no matter what you do, you're just a minute or two short of time, but there is a way. The key is to minimize the time wasted by the two slowest people by having them cross together. And because you'll need to make a couple of return trips with the lantern, you'll want to have the fastest people available to do so. So, you and the lab assistant quickly run across with the lantern, though you have to slow down a bit to match her pace. After two minutes, both of you are across, and you, as the quickest, run back with the lantern. Only three minutes have passed. So far, so good. Now comes the hard part. The professor and the janitor take the lantern and cross together. This takes them ten minutes since the janitor has to slow down for the old professor who keeps muttering that he probably shouldn't have given the zombies night vision. By the time they're across, there are only four minutes left, and you're still stuck on the wrong side of the bridge. But remember, the lab assistant has been waiting on the other side, and she's the second fastest of the group. So she grabs the lantern from the professor and runs back across to you. Now with only two minutes left, the two of you make the final crossing. As you step on the far side of the gorge, you cut the ropes and collapse the bridge behind you, just in the nick of time.
Solution:
Show Answer
At first it might seem like no matter what you do, you’re just a minute or two short of time, but there is a way. The key is to minimize the time wasted by the two slowest people by having them cross together. And because you’ll need to make a couple of return trips with the lantern, you’ll want to have the fastest people available to do so. So, you and the lab assistant quickly run across with the lantern, though you have to slow down a bit to match her pace. After two minutes, both of you are across, and you, as the quickest, run back with the lantern. Only three minutes have passed. So far, so good. Now comes the hard part. The professor and the janitor take the lantern and cross together. This takes them ten minutes since the janitor has to slow down for the old professor who keeps muttering that he probably shouldn’t have given the zombies night vision. By the time they’re across, there are only four minutes left, and you’re still stuck on the wrong side of the bridge. But remember, the lab assistant has been waiting on the other side, and she’s the second fastest of the group. So she grabs the lantern from the professor and runs back across to you. Now with only two minutes left, the two of you make the final crossing. As you step on the far side of the gorge, you cut the ropes and collapse the bridge behind you, just in the nick of time.
Show Answer
At first it might seem like no matter what you do, you’re just a minute or two short of time, but there is a way. The key is to minimize the time wasted by the two slowest people by having them cross together. And because you’ll need to make a couple of return trips with the lantern, you’ll want to have the fastest people available to do so. So, you and the lab assistant quickly run across with the lantern, though you have to slow down a bit to match her pace. After two minutes, both of you are across, and you, as the quickest, run back with the lantern. Only three minutes have passed. So far, so good. Now comes the hard part. The professor and the janitor take the lantern and cross together. This takes them ten minutes since the janitor has to slow down for the old professor who keeps muttering that he probably shouldn’t have given the zombies night vision. By the time they’re across, there are only four minutes left, and you’re still stuck on the wrong side of the bridge. But remember, the lab assistant has been waiting on the other side, and she’s the second fastest of the group. So she grabs the lantern from the professor and runs back across to you. Now with only two minutes left, the two of you make the final crossing. As you step on the far side of the gorge, you cut the ropes and collapse the bridge behind you, just in the nick of time.
The title of the problem tells you how to approach these four questions. (A). A bus leaves Moscow for Tula at noon. An hour later a cyclist leaves Tula for mosco, moving slower than the bus. When the bus and cyclist meet, which one of the two will be farther from Moscow? (B). Which is worth more: a pound of $10 gold peices or half a pound of $20 gold pieces? (C). At six o’clock the wall clock struck 6 times. Checking with my watch, I noticed the time between the first and last strokes was 30 seconds. How long will the clock take to strike 12 at midnight? (D). Three swallows fly outward from a point. When will they all be on the same plane in space? Now check the answers. Did you fall into any of the traps which lurk in these simple problems?
Answer: (A). Neither (B). A pound of metal is always more than half a pound of the same metal. (C). Six strokes took 30 seconds, therefore 12 strokes will take 60 seconds. But when the clock struck six, there were only 5 intervals between strokes, and each interval was 30/5=6 seconds. Between the first and twelfth strokes there will be 11 intervals of 6 seconds each, therefore 12 strokes will take 66 seconds. (D). There is always a plane that contains any 3 points
Solution:
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(A). Neither
(B). A pound of metal is always more than half a pound of the same metal.
(C). Six strokes took 30 seconds, therefore 12 strokes will take 60 seconds. But when the clock struck six, there were only 5 intervals between strokes, and each interval was 30/5=6 seconds. Between the first and twelfth strokes there will be 11 intervals of 6 seconds each, therefore 12 strokes will take 66 seconds.
(D). There is always a plane that contains any 3 points
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(A). Neither
(B). A pound of metal is always more than half a pound of the same metal.
(C). Six strokes took 30 seconds, therefore 12 strokes will take 60 seconds. But when the clock struck six, there were only 5 intervals between strokes, and each interval was 30/5=6 seconds. Between the first and twelfth strokes there will be 11 intervals of 6 seconds each, therefore 12 strokes will take 66 seconds.
(D). There is always a plane that contains any 3 points
(B). A pound of metal is always more than half a pound of the same metal.
(C). Six strokes took 30 seconds, therefore 12 strokes will take 60 seconds. But when the clock struck six, there were only 5 intervals between strokes, and each interval was 30/5=6 seconds. Between the first and twelfth strokes there will be 11 intervals of 6 seconds each, therefore 12 strokes will take 66 seconds.
(D). There is always a plane that contains any 3 points
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