Question

Antonio is having a party and wants to fill his swimming pool. If he only uses his hose it takes 2 hours more than if he uses only his neighbor's hose. If he uses both hoses together, the pool fills in 7.5 hours. How long does it take for each hose to fill the pool?

Answer 1

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,

`\begin{gathered} (1)/(t)+(1)/(t+2)=(1)/((15)/(2)) \\ \Rightarrow(t+2+t)/(t(t+2))=(2)/(15) \\ \Rightarrow(2t+2)/(t(t+2))=(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}`

By solving the above equation for t, we get:

`t=(13+√(229))/(2)`

Therefore, it takes 14.07 hours to fill with his neighbor's hose and it takes 16.07 hours to fill with his hose.