Let w is the width of the strip mowed by the outer mower as shown in the figure. So, the area mowed by the outer mower is the area of the shaded region.
Each wants to mow no more than half of the lawn, so, both have to mow exactly half of the area of the lawn.
The length of the rectangular lawn, [tex]l=170[/tex] feet
and the width, [tex]b=95[/tex] feet.
The dimensions [tex]( l'\times b')[/tex] of the area left to the other mower are
[tex]l'=170-2w[/tex] and [tex]b'=95-2w[/tex].
As. both most have to mow half of the lawn, so
[tex](170-2w)\times(95-2w)=\frac{170\times95}{2}[/tex]
[tex]\Rightarrow 4w^2-530w+8075=0[/tex]
[tex]\Rightarrow w=17.5641, 114.9358[/tex]
Ignoring the higher value as w cant be more than the dimension of the lawn.
So, the required width of the strip
w=17.564 feet (rounded up to three decimal places)
As the outer mower has a 24-inch cut, so in 1st trip, he cuts the 24-inch or 2 feet of required width.
So, the number of the required trip is
[tex]\frac{17.564}{2}=8.782[/tex]
=8.8 (rounded up to one decimal place)
