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# Calculus/Simultaneous equations

Question
I am really struggling with this word problem, I have trouble in setting up the expressions.
you have a pool with 3 pipes to fill it with.
pipes A and B take 4hrs to fill the pool,
pipes B and C take 3.75hrs to fill the pool,
and
pipes A, B, and C take 3hrs.
how many hours would it take each pipe individually to fill the pool.

Questioner:Roger
Country:Iowa, United States
Category:Calculus
Private:No
Subject:pre-calc
Question:

I am really struggling with this word problem, I have trouble in setting up the expressions.
you have a pool with 3 pipes to fill it with.
pipes A and B take 4hrs to fill the pool,
pipes B and C take 3.75hrs to fill the pool,
and
pipes A, B, and C take 3hrs.
how many hours would it take each pipe individually to fill the pool.
....................................................
Try this approach:

Let a = the flow rate of pipe A, in pph.*
b = ......................B.........
c = ......................C.........

* pph = 'pools per hour'

pipes A and B take 4hrs to fill the pool, means:
a + b = 1/4  pph

pipes B and C take 3.75hrs to fill the pool,means
b + c = 1/3.75 = 4/15  pph

and
pipes A, B, and C take 3hrs, means
a + b + c = 1/3   pph

Now you have three equations in three variables -- clear fractions and solve.

Calculus

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#### Paul Klarreich

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All topics in first-year calculus including infinite series, max-min and related rate problems. Also trigonometry and complex numbers, theory of equations, exponential and logarithmic functions. I can also try (but not guarantee) to answer questions on Analysis -- sequences, limits, continuity.

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