Draft a polynomial function.

[earthboundslave]

There are three water pipes A, B and C each with water flowing at a constant speed.
If the pipes are used individually to fill up an empty pool, pipe A takes 5 more hours to fill it up than pipe B,
while pipe C takes 2 more hours than pipe B. If the three pipes are used simultaneously,
they take 4 hours to fill up the pool.
Suppose pipe B alone takes x hours to fill up the pool.

(a) Prove that x³ - 5x² - 46x - 40 = 0
(b) Hence find x by factorizing x³ - 5² - 46x - 40 = 0 .

For part(b), since the function is already there, it is easy.

However, I have absolutely no idea how to draft the function in part(a).

The question only give x as time but no other factors like volume, speed etc. When I tried to draft a function f(x), I don't know what its physical meaning would be in this question. Therefore I have no clue how to use the variable x(time) to draft the function stated in part(a).

 

[Deleted member 4993]

There are three water pipes A, B and C each with water flowing at a constant speed.
If the pipes are used individually to fill up an empty pool, pipe A takes 5 more hours to fill it up than pipe B,
while pipe C takes 2 more hours than pipe B. If the three pipes are used simultaneously,
they take 4 hours to fill up the pool.
Suppose pipe B alone takes x hours to fill up the pool.

(a) Prove that x³ - 5x² - 46x - 40 = 0
(b) Hence find x by factorizing x³ - 5² - 46x - 40 = 0 .

For part(b), since the function is already there, it is easy.

However, I have absolutely no idea how to draft the function in part(a).

The question only give x as time but no other factors like volume, speed etc. When I tried to draft a function f(x), I don't know what its physical meaning would be in this question. Therefore I have no clue how to use the variable x(time) to draft the function stated in part(a).

The volume of the pool really does not matter. It will factor out. To be comfortable with your thoughts - start with assuming the volume to be 'V'.

The flow rate of B is = V/x
The flow rate of A is = V/(x+5)
The flow rate of C is = V/(x+2)

Combined flow rate (of A, B & C) is = V/4

So:

V/x + V/(x+5) + V/(x+2) = V/x

Factor out 'V' from both sides to get:

1/x + 1/(x+5) + 1/(x+2) = 1/x

Now continue to simplify......