I need help with an answer to locate a geocache and I am stumped, they're math problems and very challenging.?
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I need help with an answer to locate a geocache and I am stumped, they're math problems and very challenging.?

[From: ] [author: ] [Date: 14-03-06] [Hit: ]
of which 5 are captured, tagged, and then released. A certain time later 4 of 15 elk are captured.Assuming the elk are captured independently of one another and that each elk has the same chance of being captured, what is the probability that exactly 2 or these 4 elk have been tagged?......
1. Each valve is A, B, and C, when open, releases water into a tank at its own constant rate. With all three valves open, the tank fills in 1 hour, with only valves A and C open it will take 1.5 hours, and with only valves B and C open it takes 2 hours. How many minutes will it take to fill the tank with only valves A and B open? Answer: AB

I also have an additional problem to solve to get some coordinates.

2. A forest contains 15 elk, of which 5 are captured, tagged, and then released. A certain time later 4 of 15 elk are captured. Assuming the elk are captured independently of one another and that each elk has the same chance of being captured, what is the probability that exactly 2 or these 4 elk have been tagged? Express the answer as a common fraction. Answer: CD/EF

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The website below gets you part way there, is shows that by themselves

Valve A fills a tank in 2 hours

Valve B fills a tank in 3 hours

Valve C fills a tank in 6 hours

You want to know how long with A & B together

A fills a tank in 2 hours, so it fills 1/2 tank per hour

B fills a tank in 3 hours, so it fills 1/3 tank per hour

When working together, they fill

1/2 + 1/3 tank per hour or

3/6 + 2/6 tank per hour = 5/6 tanks per hour

If they fill 5/6 tanks per hour, it will tank them 6/5 hours to fill 1 tank

6/5 hours * 60 minutes per hour = 360/5 minutes = 72 minutes, that is your answer

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1. remember:
if it takes say 2 hrs to complete a task then 1/2 the task is completed in 1 hour

if it takes 3/2 hrs to complete a task then 2/3 of the task is completed in 1 hour

1/a + 1/b + 1/c = 1
1/a + 1/c = 2/3
1/b + 1/c = 1/2

subtract eq3 from eq2 to get:
1/a - 1/b = 1/6
1/b = 1/a - 1/6

1/a + 1/c = 2/3
1/c = 2/3 - 1/a

1/a + 1/b + 1/c = 1
1/a + (1/a - 1/6) + (2/3 - 1/a) = 1
1/a + 1/a - 1/6 + 4/6 - 1/a = 1
1/a + 3/6 = 6/6
1/a = 3/6
a = 2

1/a + 1/c = 2/3
1/2 + 1/c = 2/3
1/c = 1/6
c = 6

1/b + 1/c = 1/2
1/b + 1/6 = 3/6
1/b = 2/6
b = 3

1/a + 1/b = 1
x(1/2 + 1/3) = 1
x(3/6 + 2/6) = 1
(5/6)x = 1
x = 6/5 hrs
x = 72 min

2. (C[5,2] * C[10,2]) / (C[15,4]) = 450/1365 = 30/91
1
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