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} (1)/(A)*8+(1)/(B)*8=1, \\ A=B+10. \end{gathered}`

Substituting the second equation in the first one we get:

`(8)/(B+10)+(8)/(B)=1.`

Simplifying the above result we get:

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

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

`\begin{gathered} (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=(6\pm√((-6)^2-4*1(-80)))/(2*1)=(6\pm√(36+320))/(2) \\ =(6\pm√(4*89))/(2)=3\pm√(89). \end{gathered}`

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

`B=3+√(89)\approx12.4.`

Answer: 12.4 hours.