Question

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 broomhilda to accomplish the same task working alone? write your answer as an exact fraction or decimal rounded to tenths. broomhildas time = question help: video

Explanation:

Step1: Determine Hanz's time in terms of Broomhilda's time

Since Hanz works at one - quarter of Broomhilda's speed, if Broomhilda's time is $B$, then Hanz's time is $4B$ because work rate and time are inversely proportional.

Step2: Calculate work - rates

The work - rate of Broomhilda is $\frac{1}{B}$ (fraction of the task completed per hour) and the work - rate of Hanz is $\frac{1}{4B}$. When they work together, their combined work - rate is $\frac{1}{6}$ (since they complete the task in 6 hours).

Step3: Set up the equation for combined work - rate

The sum of their individual work - rates equals their combined work - rate. So, $\frac{1}{B}+\frac{1}{4B}=\frac{1}{6}$.
Combining the left - hand side: $\frac{4 + 1}{4B}=\frac{5}{4B}$.
So, $\frac{5}{4B}=\frac{1}{6}$.

Step4: Solve for B

Cross - multiply to get $4B\times1=5\times6$.
$4B = 30$.
$B=\frac{30}{4}=7.5$.

Answer:

Hanz (in terms of $B$) = $4B$
Broomhilda's Time = $7.5$