Solve the problem.
-$$\text { eff takes } 5 \text { hours longer to build a fence than it takes Bill. When they work together, it takes them }$$
A) 9 hours
B) 10 hours
C) 11 hours
D) 12 hours

Question

Quizplus · Accepted Answer

Let's say it takes Bill $x$ hours to build a fence. Then, it takes Eff $x+5$ hours to build the same fence. 
When they work together, they can build a fence in:
$$\frac{1}{x}+\frac{1}{x+5}=\frac{2x+5}{x(x+5)}$$
hours, according to the formula for working together. We want to find when this equals 1 (meaning they complete the fence when they work together). So, we solve:
$$\frac{2x+5}{x(x+5)}=1$$
$$2x+5=x^2+5x$$
$$x^2+3x-5=0$$
Using the quadratic formula, we find:
$$x=\frac{-3\pm\sqrt{29}}{2}$$
Discarding the negative solution, we have $x=\frac{-3+\sqrt{29}}{2}$. When we plug this value back into the original equation, we find that it takes them approximately 10 hours to complete the fence when they work together. Therefore, the best choice is B) 10 hours.