# MathA worm is at the bottom of a forty meter hole. It can crawl upwards at the rate of four meters in one day, but at night, it slips back three meters. At this rate, how long will it take the worm...

A worm is at the bottom of a forty meter hole. It can crawl upwards at the rate of four meters in one day, but at night, it slips back three meters. At this rate, how long will it take the worm to crawl out of the hole?

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I did the math out and I agree with pohnpei that on day 37, the worm hits the 40 meter mark and should be able to get out of the hole.

Basically, the worm gains one meter per day, because he climbs 4 and slides back 3, and 4-3=1. So the morning of day 37, when the worm begins at 36 meters from the bottom, it will climb the last 4 meters and exit from the hole.

I think it should take it 37 days. It should make it out of the hole on the 37th day because it will get out of the hole before night and so it won't slip back. On day 36, it should get up to 39 meters and slip back to 36 meters in the night. On day 37, it will go up 4 more meters and get out of the hole.

Yes, it is pretty simple. You solve this by taking the total distance the worm travels and subtracting the amount it slips back. Four minus three is one. So it climbs a meter a day, but on the last day it won't slip back and it gets out. Persistent worm!

37 days, because on day 37 it crawls up to the top.

I hope it doesn't slide down again though ^ ^

And well, it's very slow! >__<

On the 36th day he only gets up to 39m (before sliding back to 36). Each day has a net gain of 1m, so his starting point on any given day is x-1m, where x is the number of days. He starts at 0m on day 1, 1m on day 2, etc. Therefore the highest point he reaches on any given day is x-1+4, or x+3. So on the first day he gets to four metres, on the second he gets to five, on the third he gets to six and so on. It isn't until the 37th day that he reaches the top of the hole.

Well, if you got 37 days, you are right.

At the end of day one, the worm would be at the one meter mark. At the end of the 35th day, the worm would be at the 35th meter mark. On the 36th day, the worm travels from 35 meters to 39 meters but slips back to 36 meters at the end of the 36th day. On the 37th day, the worm travels up 4 meters from the 36th meter and is consequently out of the hole!