STEP - BY - STEP - EXPLANATION
What to find?
The time taken for each person to mow the lawn alone.
Given:
Time take for the two to mow the lawn together = 60 minutes.
Brian could mow himself 22 minutes more than it would take andy.
Let x be the time taken for Andy to mow the lawn.
Let x + 22 be the time taken for Brian to mow the lawn.
Step 1
Form the equation.
[tex](\frac{1}{x}+\frac{1}{x+22})\times60=1[/tex]Step 2
Divide both-side of the equation by 60.
[tex]\frac{1}{x}+\frac{1}{x+22}=\frac{1}{60}[/tex][tex]\frac{x+22+x}{x(x+22)}=\frac{1}{60}[/tex][tex]\frac{2x+22}{x^2+22x}=\frac{1}{60}[/tex]Step 3
Cross-multiply.
[tex]x^2+22x=60(2x+22)[/tex]Step 4
Open the parenthesis.
[tex]x^2+22x=120x+1320[/tex][tex]x^2+22x-120x-1320=0[/tex][tex]x^2-98x-1320=0[/tex]Step 5
Solve the above using factorization method.
[tex]\begin{gathered} x^2-110x+12x-1320=0 \\ \\ x(x-110)+12(x-110)=0 \\ \\ (x-110)(x+12)=0 \end{gathered}[/tex]Either (x-110) = 0 or x+12 =0
x =110 or x =-12
Since there is no negative timing, we will consider only the positive value.
Hence, x=110
Therefore,
The time taken Andy to mow = 110 minutes.
The time taken for Brian to mow = x+ 22 = 110+22 = 132
ANSWER
It takes Brian 132 minutes to mow the lawn himself.
It takes Andy 110 minutes to mow the lawn himself.
