Answer:
Step-by-step explanation:
this problem focuses on the combined work rate
both can finish the work under 63 minute
let bobby mow the lawn in x minute
Billy will then mow the lawn in x-25 minutes
Let the completed job = 1 (a mowed lawn)
we can now apply the combined work formula for the two boys as
[tex]\frac{63}{x}+\frac{63}{x-25}=1[/tex]
multiplying through by x(x-25 )we have
[tex]63(x-25)+63x= x(x-25)[/tex]
open bracket we have
[tex]63x-1575+63x= x^2-25x[/tex]
rearranging and collecting like terms we have
[tex]0=x^2-25x-63x-63x+1575 \\\\0=x^2-151x+1575 \\\\x^2-151x+1575=0[/tex]
we can now use the quadractic formula
[tex]x=\frac{-b\frac{+}{} \sqrt{b^2-4ac} }{2a}[/tex]
a= 1
b= -151
c= 1575
[tex]x=\frac{-(-151)\frac{+}{} \sqrt{151^2-4*1*1575} }{2*1}[/tex]
[tex]x=\frac{-(-151)\frac{+}{} \sqrt{22801-6300} }{2} \\\\x=\frac{-(-151)\frac{+}{} \sqrt{16501} }{2} \\\\x=\frac{-(-151)\frac{+}{} 128.45}{2} \\\\[/tex]
[tex]x=\frac{-(-151)+128.45}{2} \\\\\x=\frac{279.45}{2} \\\\x=139.72 \\\\\\x=\frac{-(-151)-128.45}{2}\\\\x=\frac{151-128.45}{2}\\\\x=\frac{22.55}{2}\\\\x=11.27[/tex]
the first answer x= 139.72 approximately 140 minutes mins is correct for Bobby's time
let us check
[tex]\frac{63}{140}+\frac{63}{140-25}=1\\\\\\0.45+\frac{63}{115} =1\\\\0.45+0.5478=1\\0.997 =1[/tex]
we can see that the solution approximates to 1
