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Seems to me that one logical approach is to determine the combined fill rates, and then work backwards from that rate to determine the time to fill one pool.
For example, the two fill rates are: 1 pool per 24 hours, and 1 pool per 8 hours. Combined, the math is 1/24 + 1/8 = 4/24. In human speak, that means the combined fill rate is 4 pools can be filled every 24 hours. Simplified to 1 pool, that's 1 pool filled every 6 hours.
For example, the two fill rates are: 1 pool per 24 hours, and 1 pool per 8 hours. Combined, the math is 1/24 + 1/8 = 4/24. In human speak, that means the combined fill rate is 4 pools can be filled every 24 hours. Simplified to 1 pool, that's 1 pool filled every 6 hours.
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I just wanted to say how much I really enjoyed this thread!!
Although it's obvious I'm not attempting to answer the question (cough, cough
), it's really a lot of fun and quite interesting to read how people have come up with the answer. Unfortunately, math taps into the part of my brain that either isn't there or just doesn't work.
But I think this would be an awesome idea for a regular thread series: "Math Problem of the Week" or general problems that people could offer their solutions to... (Wallpapering? Changing out the hardware in the back of your toilet? Keeping plants alive? Not that any of this would apply to me... Again... cough, cough, cough.)
It was just really cool to see everyone dig in and come up with their own answers. Even the non-math-related ones!
Although it's obvious I'm not attempting to answer the question (cough, cough
), it's really a lot of fun and quite interesting to read how people have come up with the answer. Unfortunately, math taps into the part of my brain that either isn't there or just doesn't work. But I think this would be an awesome idea for a regular thread series: "Math Problem of the Week" or general problems that people could offer their solutions to... (Wallpapering? Changing out the hardware in the back of your toilet? Keeping plants alive? Not that any of this would apply to me... Again... cough, cough, cough.)
It was just really cool to see everyone dig in and come up with their own answers. Even the non-math-related ones!
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As a veteran house remodel-er, and a decent plumber, I must protest the ruling. (I am sure Oncefallen will back me up on this)
We have to know the pipe setup, to know if both faucets will pump at their individual capacity when both are on. We'll need to see the pump rating as well, if the swimming pool isn't on a water main.
Also, the rate of evaporation is a constant, assuming constant temperature and humidity. Therefore the two faucets will fill faster than the combined capacity.
the correct answer is already posted but being a math geek, i want to work it out for myself too
let x be the rate of the first faucet, y the rate of the second faucet, in units-per-hour
and let z be the volume of the pool in units.
then 24*x = z = 8*y
so x = z/24
and y = z/8
let t be the time it takes to fill up the pool with both faucets.
then
x*t + y*t = z
or making substitutions,
(z/24)*t + (z/8)*t = z
z*(1/24 +1/8) = z/t
(1/24 + 3/24) = 1/t
4/24 = 1/6 = 1/t
→ t = 6 hours
let x be the rate of the first faucet, y the rate of the second faucet, in units-per-hour
and let z be the volume of the pool in units.
then 24*x = z = 8*y
so x = z/24
and y = z/8
let t be the time it takes to fill up the pool with both faucets.
then
x*t + y*t = z
or making substitutions,
(z/24)*t + (z/8)*t = z
z*(1/24 +1/8) = z/t
(1/24 + 3/24) = 1/t
4/24 = 1/6 = 1/t
→ t = 6 hours
