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
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
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
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