Answer :
Answer:
A takes 14 hours and B takes 10 hours in working alone.
Step-by-step explanation:
Let the time taken by B alone = x hours,
One hour work of B = [tex]\frac{1}{x}[/tex]
∵ fishermen A, working alone, takes 4 hours longer to run the hoop nets than it takes fisherman B working alone.
So, the time taken by A alone = (x+4) hours,
One hour work of A = [tex]\frac{1}{x+4}[/tex]
Thus, total one hour when A and B work simultaneously = [tex]\frac{1}{x}+\frac{1}{x+4}[/tex]
Since, together they take [tex]5\frac{5}{6}[/tex] hours
Total one hour work = [tex]\frac{1}{5\frac{5}{6}}=\frac{1}{\frac{35}{6}}=\frac{6}{35}[/tex]
[tex]\implies \frac{1}{x}+\frac{1}{x+4}=\frac{6}{35}[/tex]
[tex]\frac{x+4+x}{x^2+4x}=\frac{6}{35}[/tex]
[tex]\frac{2x+4}{x^2+4x}=\frac{6}{35}[/tex]
[tex]70x + 140 = 6x^2 + 24x[/tex]
[tex]6x^2 + 24x - 70x - 140=0[/tex]
[tex]6x^2 - 46x - 140=0[/tex]
[tex]3x^2 - 23x - 70=0[/tex]
[tex]3x^2-(30-7)x - 70=0[/tex] ( Middle term splitting )
[tex]3x^2 - 30x + 7x - 70=0[/tex]
[tex]3x(x-10) + 7(x-10)=0[/tex]
[tex](3x+7)(x-10)=0[/tex]
By zero product property,
3x + 7 = 0 or x - 10 =0
⇒ x = -7/3 ( not possible ) or x = 10
Hence, time taken by B = 10 hours,
Time taken by A = 10 + 4 = 14 hours