Question

working together, stefan and jade can collect and bale the hay field in 6.15 hours. if jade worked alone, it would have taken her 16 hours. how long would it take stefan to do it alone?
7.98 hours
9.99 hours
10.27 hours
12.83 hours

Explanation:

Step1: Define work - rate

Let the total work be 1. The combined work - rate of Stefan and Jade is $\frac{1}{6.15}$ (since they complete 1 work in 6.15 hours). Jade's work - rate is $\frac{1}{16}$ (since she completes 1 work in 16 hours). Let Stefan's work - rate be $\frac{1}{x}$, where $x$ is the number of hours Stefan takes to complete the work alone.

Step2: Set up the equation

The combined work - rate of Stefan and Jade is the sum of their individual work - rates. So, $\frac{1}{6.15}=\frac{1}{16}+\frac{1}{x}$.

Step3: Solve for $\frac{1}{x}$

$\frac{1}{x}=\frac{1}{6.15}-\frac{1}{16}$. First, find a common denominator for the right - hand side. The common denominator of 6.15 and 16 is $6.15\times16 = 98.4$. Then $\frac{1}{6.15}-\frac{1}{16}=\frac{16}{98.4}-\frac{6.15}{98.4}=\frac{16 - 6.15}{98.4}=\frac{9.85}{98.4}\approx0.0999$.

Step4: Solve for $x$

Since $\frac{1}{x}=0.0999$, then $x=\frac{1}{0.0999}\approx10.01\approx9.99$ (due to rounding differences in the intermediate steps).

Answer:

B. 9.99 hours