Question

a small pump takes 6 more hours than a large pump to empty a city swimming pool. the rate for the large pump to drain the pool can be represented by the rational expression \\(\frac{1}{x}\\) where x is the time that it takes for the large pump to drain the pool.

a. write a simplified rational expression that describes the combined rate if both pumps are used to drain the pool
b. what is the combined rate to drain the pool if it takes the larger pump 8 hours to drain the pool?

a. the simplified rational expression that describes the combined rate if both pumps are used to drain the pool is
(type your answer in factored form. use integers or fractions for any numbers in the expression.)

Explanation:

Define the individual rates of the pumps

$$
LATEXBLOCK0
$$

Find the combined rate expression (part a)

$$
LATEXBLOCK1
$$

Calculate the combined rate when \(x = 8\) (part b)

$$
LATEXBLOCK2
$$

Answer:

Question a

The simplified rational expression that describes the combined rate if both pumps are used to drain the pool is <blank>\(\frac{2(x+3)}{x(x+6)}\)</blank>.

Question b

The combined rate to drain the pool if it takes the larger pump 8 hours to drain the pool is <blank>\(\frac{11}{56}\)</blank>.