Question

Two companies working together can clear a parcel of land in 8 hours. Working alone, it would take Company A 10 hours longer to clearthe land than it would Company B. How long would it take Company B to clear the parcel of land alone? (Round your answer to thenearest tenth.)

Answer 1

To answer this question we will set and solve a system of equations.

Let A be the time (in hours) that it would take Company A to clear the parcel of land alone, and B be the time (in hours) that it would take Company B to clear the parcel of land alone.

Since working together, the two companies can clear the parcel of land in 8 hours, and wirking alone, it would take Company A 10 hours longer than Company B, then we can set the following system of equations:

$\begin{gathered} \frac{1}{A}*8+\frac{1}{B}*8=1, \\ A=B+10. \end{gathered}$

Substituting the second equation in the first one we get:

$\frac{8}{B+10}+\frac{8}{B}=1.$

Simplifying the above result we get:

$\begin{gathered} \frac{8B}{(B+10)B}+\frac{8(B+10)}{(B+10)B}=1, \\ \frac{16B+80}{(B+10)B}=1. \end{gathered}$

Multiplying the above result by (B+10)B we get:

$\begin{gathered} \frac{16B+80}{(B+10)B}*(B+10)B=1*(B+10)B, \\ 16B+80=(B+10)B. \end{gathered}$

Simplifying the above result we get:

$16B+80=B^2+10B.$

Subtracting 16B+80 from the above result we get:

$\begin{gathered} 16B+80-(16B+80)=B^2+10B-(16B+80), \\ 0=B^2-6B-80. \end{gathered}$

Using the quadratic formula we get:

$\begin{gathered} B=\frac{6\pm\sqrt{(-6)^2-4*1(-80)}}{2*1}=\frac{6\pm\sqrt{36+320}}{2} \\ =\frac{6\pm\sqrt{4*89}}{2}=3\pm\sqrt{89}. \end{gathered}$

Since a negative value of B has no real meaning, we get that:

$B=3+\sqrt{89}\approx12.4.$

Answer: 12.4 hours.