I REALLY need help on this math problem please! It is hard! I tried though. Can you solve it?

Question

Tom and Eileen are on nature walk. They come to a stream and find two buckets. One is marked four gallons and teh other is marked 9 gallons. The buckets have no other markings. Tom and Eileen start talking about how many different gallon amounts they could measure with the two buckets. Tom says you could only measure 4 gallons, 9 gallons, and 13 gallons. Eileen agrees that the total of the two buckets is the most you could measure, but argues that you could find other gallon amonts also. (For example, she says that if you fill the 9 gallon bucket, and pour 4 gallons out into the 4 gallon bucket, you'd have 5 gallons left in the 9 gallon bucket. 1. How many different gallon amounts can you find that you can measure using only these two buckets? (That is, you have no other containers and no other ways to make measurements. You cannot even make a mark on a bucket. There is no way to tell when a bucket is half way full.) Explain how you arived at each gallon amount and justify your answer

Answer 1

Not to bad:
1&5 gallons: Fill up 9 gallon bucket(bucket 1): use it to fill up 4 gallon bucket(bucket 2)(there are 5 gallons left in bucket 1) empty bucket 2 and pour remaining water in bucket 1 into bucket 2: (now there is one gallon in bucket 1)

6 gallons: empty bucket 2: Since you have one gallon in bucket 1 pour that into bucket 2. Fill up bucket 1. you now have one gallon in bucket 2 and 9 gallons in bucket 1. Fill up bucket 2 from bucket 1. Now there is 6 gallons in bucket 1.

2 gallons: Now you have 4 gallons in bucket 2 and 6 gallons in bucket 1. empty bucket 2. Fill up bucket 2 from bucket 1. Now you have 4 gallons in bucket 2 and two gallons left in bucket 1.

7 gallons: empty bucket 2 again. Pour the remaining 2 gallons into bucket 2. Fill up bucket 1. Now you have 2 gallons in bucket 2 and 9 gallons in bucket 1. Fill up bucket 2 from bucket 1. Now you have 4 gallons ini bucket 2 and 7 gallons left in bucket 1.

3 gallons: empty bucket 2 and fill it up from bucket 1 remaining 7 gallons. Now you have 3 gallons left in bucket 1.

8 gallons: empty bucket 2 and fill with remaining 3 gallons from bucket 1. Fill bucket 1 then use it to fill bucket 2. Now you have 8 gallons in bucket 1

There you have it 1-13 gallons can be determined. You get 10, 11 and 12 in the above when bucket 2 has partially full and bucket 1 is full.

Answer 2

Well obviously the 4 gallons, 9 gallons and 13 gallons make sense. The argument for 5 gallons would work as well. The only other measurement I can think of right now would be 1 gallon. If you fill the 9 gallon and pour it into the 4 gallon you now have 5 gallons in the 9 gallon bucket. If you dump out the 4 gallon bucket and pour the five gallons into it, the remainder in the 9 gallon bucket is 1 gallon. Oh and of course you can measure 8 gallons by filling the 4 gallon bucket 2 times and pouring it into the 9 gallon. And for that matter if you have 8 gallons in the one bucket, you can put another 4 gallons in the original bucket and have 12 gallons.
So I'd say, 1,4,5,8,9,12,13

Answer 3

This is an interesting one...
let's see...I hope I thought of them all. If not, well it was a good college try.

1 gallon - filling the 9 gal bucket, pouring out 4 gal, dumping out the 4 gal and then filling the 4 gal bucket again...that will leave you with 1 gal left in the 9 gallon bucket.

4 gallons - obviously

5 gallons - fill nine, empty into 4 gal

8 gallons - fill nine by dumping the 4 gal into it twice

9 gallons - obviously

10 gallons - following the same procedure for finding 1 gallon, then putting that 1 gallon into the four gal bucket and filling the 9 gallon bucket.

12 gallons - following the same procedure for finding 8 gallons, then fill the 4 gallon bucket again

13 gallons - obvious

Answer 4

9 gallons- use the 9 gallon bucket
4 gallons- use the 4 gallon bucket
13 gallons- use both buckets
5 gallons- use the example described

So that's 4 ways =)

Here's another
Once you have 5 gallons in the 9 gallon bucket
Dump 4 back into the 4 gallon.
You're left with 1 gallon in the 9 gallon bucket.

Answer 5

Answered this for "taylor_travers098". Do you know this poster? Check her answers.

Answer 6

Do your own homework.