Question

i can identify domain restrictions of rational expressions and equations.
i can add and subtract rational expressions by finding a common denominator.
broomhilda von choppy is a veteran butcher who swept all categories of the austrian bull carving tournament of 2009. hanz is her young and inexperienced man - servant who works at only one quarter of her speed.
hint: you may find it useful to think about the ratio between hanz and broomhildas times. let broomhildas time be b, and write hanzs time as an equation that uses b:
broomhilda = b
hanz (in terms of b) =
when working together, the two of them fully carve and package an adult bull in 6 hours. how many hours would it take hanz to accomplish the same task working alone? write your answer as an exact fraction or decimal rounded to tenths.
hanzs time =

Explanation:

Step1: Determine Hanz's time in terms of B

Since Hanz works at one - quarter of Broomhilda's speed, if work = rate×time and the work is the same for both, and rate and time are inversely proportional. So if Broomhilda's time is $B$, Hanz's time is $4B$.

Step2: Calculate work - rates

The work - rate of Broomhilda is $\frac{1}{B}$ (work per hour) and the work - rate of Hanz is $\frac{1}{4B}$ (work per hour). When they work together, their combined work - rate is $\frac{1}{B}+\frac{1}{4B}=\frac{4 + 1}{4B}=\frac{5}{4B}$.

Step3: Use the combined - work information

We know that when they work together, they complete the work in 6 hours. So their combined work - rate is $\frac{1}{6}$ (work per hour). Then we set up the equation $\frac{5}{4B}=\frac{1}{6}$.
Cross - multiply to get $4B\times1 = 5\times6$, so $4B=30$, and $B = 7.5$.

Step4: Find Hanz's time

Since Hanz's time is $4B$, substituting $B = 7.5$ into it, we get Hanz's time $=4\times7.5 = 30$ hours.

Answer:

30