Answer :
Let x be the rate at which Maria can assemble a bicycle, and y the rate at which Brandon can assemble a bicycle, then we can set the following equation:
[tex]3y+4x=1.[/tex]Now, we know that Maria takes 2 hours more to assemble a bicycle on her own, therefore:
[tex]\frac{1}{x}-2=\frac{1}{y}\text{.}[/tex]Solving the above equation, for y, we get:
[tex]\begin{gathered} \frac{1-2x}{x}=\frac{1}{y}, \\ y=\frac{x}{1-2x}\text{.} \end{gathered}[/tex]Substituting the above result in the first equation, we get:
[tex]3(\frac{x}{1-2x})+4x=1.[/tex]Solving the above equation for x, we get:
[tex]\begin{gathered} \frac{3x}{1-2x}+4x=1, \\ 3x+4x(1-2x)=1-2x, \\ 3x+4x-8x^2=1-2x, \\ -8x^2+7x=1-2x, \\ -8x^2+9x-1=0. \end{gathered}[/tex]Using the quadratic formula, we get:
[tex]\begin{gathered} x_1=1, \\ x_2=\frac{1}{8}\text{.} \end{gathered}[/tex]The first solution for x has no meaning in this context because that would imply that Maria can assemble the bicycle in 1 hour and that Brandon can assemble one in 2 hours less than that, therefore, Maria can assemble 1 bicycle in 8 hours.
Answer:
[tex]8.[/tex]