To find:
How long it takes for each hose to fill the pool.
Solution:
Let it takes t hours to fill the swimming pool if he use neighbour's hose then it takes t + 2 hours to fill the swimming pool if he uses his hose.
Given that he used both hoses together, the pool fills in 7.5 hours. So,
[tex]\begin{gathered} \frac{1}{t}+\frac{1}{t+2}=\frac{1}{\frac{15}{2}} \\ \Rightarrow\frac{t+2+t}{t(t+2)}=\frac{2}{15} \\ \Rightarrow\frac{2t+2}{t(t+2)}=\frac{2}{15} \\ \Rightarrow15(2t+2)=2t(t+2) \\ \Rightarrow30t+30=2t^2+4t \\ \Rightarrow2t^2-26t-30=0 \\ \Rightarrow t^2-13t-15=0 \end{gathered}[/tex]By solving the above equation for t, we get:
[tex]t=\frac{13+\sqrt{229}}{2}[/tex]Therefore, it takes 14.07 hours to fill with his neighbor's hose and it takes 16.07 hours to fill with his hose.
