Urgent maths questions

Karn · 2010-03-15 00:02:22

A frog down the bottom of a well is able to climb up 5 metres in one hour. However, the frog then has to rest for an hour in which time it slides back 3 metres in the next hour before resting and sliding back 3 metres in the hour after that and so on.

1) Intially the frog is at the bottom of a well is 21 mtres deep. How long does it take to get out of the well: I got 17 hours

2) if the well was 26 metres deep

I got 23 hours

3) can you find the rule which connects the depth of the well to a the time it takes to get out : I dont get this one/

Then there is a Table

Depth Time
1 1
2 1
3 1
4 1
5 1
6 3
7 3
8 5
9
10
11
12
13
14
15
16
17
18
19
20

I get the 5 1s part but not the rest

Plase help thank you for any hel

Last edited by Karn (2010-03-15 00:03:02)

mathsyperson · 2010-03-15 05:44:45

You clearly understand what is going on in the question, because you got the first two answers right.
How did you get to them?

(I wouldn't worry too much about finding an exact formula, since the rule doesn't translate to an equation very well. I've got one written down, but it's not pretty.)

soroban · 2010-03-15 05:47:05

.

. .

. . . I got 17 hours . Right!

. . . I got 23 hours . Yes!

. .

. .

.

bobbym · 2010-03-15 11:04:10

Hi;

Somewhat different if you relate distance to time;

1 -> 5
2 -> 2
3 -> 7
4 -> 4
5 -> 9
6 -> 6
...

Then you can see when t is even his distance up the well is t and when it is odd his distance up the well is t + 4.

So for 17 m at 13 hours he is out. And at 12345 m he is out in 12341 hours, and at 1000 m it takes 997 hours to get out. Meaning at m>3 and m being odd subtract 4 from m to get the hours and at m even then subtract 3 to get the hours.

Random-ness · 2012-06-19 01:09:57

How do you actually find the rule/ equation with the given information?
Like how do you find out {2 D/2 - 3 if D > 5}?
What determines the number 2?
Really do need this answer as soon as possible.
Thanks

bobbym · 2012-06-19 01:18:50

Hi Random-ness;

Welcome to the forum. It helps to make the chart. Also, did you see my answer?

Random-ness · 2012-06-19 01:24:05

Yes, i do understand that part of the question though, once again i must ask how do you aquire the '2' in the function?

bobbym · 2012-06-19 01:29:25

Hi;

He just curve fit experimentally by hand to come up with that formula. It may not be the only such formula that fits that data.

Random-ness · 2012-06-19 01:39:14

So does that mean that for this particular question, there isn't really a rule/equation with 'x' and 'y'?

bobbym · 2012-06-19 01:41:40

Hi;

Notice that he had to use the greatest integer function. This means that his answer is not a linear equation like y = 3x + 5 is. As I said there may be a simpler answer than his equation.

Random-ness · 2012-06-19 01:43:35

Don't mean to be annoying but then do you have an equation for it and not just like a word explanation??
Sorry..

bobbym · 2012-06-19 01:44:58

Hi;

Do not worry, you are not being annoying. Let's work on his formula and see what can be done.

First, do you agree with his answer?

Random-ness · 2012-06-19 01:47:33

It does kinda make sense but if I had to work it out from just the given information, I wouldn't be able to do it because like you said- he sort of guessed and checked or whatever..?

bobbym · 2012-06-19 01:51:22

Hi;

Let's make a little chart that we can make with a pencil and paper.

This calculation shows that the frog will be out in t = 17 hours.

Now look at the the depths in meters that are even.

Bob · 2012-06-19 01:56:23

hi all,

True to my practice I've made a graph.

From this you can see there's not one easy function, but you could have two (odd and even depths)

Bob

bobbym · 2012-06-19 02:05:07

Hi;

The simplest is to make two equations:

When d is even then t = d - 3

When d is odd then t = d - 4

That is what I did in post #4. Soroban's method just combines this into one equation.

If you are determined to have only one equation then:

where d is the depth in meters and t is the time in hours to get out.

Random-ness · 2012-06-19 23:03:39

Dear all,

Thank you for all you help
It was much appreciated

bobbym · 2012-06-19 23:06:22

Hi Random-ness;

You are welcome. Glad to help.

Math Is Fun Forum

#1 2010-03-15 00:02:22

Urgent maths questions

#2 2010-03-15 05:44:45

Re: Urgent maths questions

#3 2010-03-15 05:47:05

Re: Urgent maths questions

#4 2010-03-15 11:04:10

Re: Urgent maths questions

#5 2012-06-19 01:09:57

Re: Urgent maths questions

#6 2012-06-19 01:18:50

Re: Urgent maths questions

#7 2012-06-19 01:24:05

Re: Urgent maths questions

#8 2012-06-19 01:29:25

Re: Urgent maths questions

#9 2012-06-19 01:39:14

Re: Urgent maths questions

#10 2012-06-19 01:41:40

Re: Urgent maths questions

#11 2012-06-19 01:43:35

Re: Urgent maths questions

#12 2012-06-19 01:44:58

Re: Urgent maths questions

#13 2012-06-19 01:47:33

Re: Urgent maths questions

#14 2012-06-19 01:51:22

Re: Urgent maths questions

#15 2012-06-19 01:56:23

Re: Urgent maths questions

#16 2012-06-19 02:05:07

Re: Urgent maths questions

#17 2012-06-19 23:03:39

Re: Urgent maths questions

#18 2012-06-19 23:06:22

Re: Urgent maths questions

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