Question

A swimming pool can be filled by either or both of two pipes of different diameters. it takes the smaller pipe twice the time that the larger pipe takes to fill the pool. if water flows through both pipes it take 213 hours to fill the pool. how long will it take the larger pipe to fill the pool? [hint: let x be the amount of the pool filled by the small pipe in one hour]

Answer 1

X+y= 213
X=2y

2y+ y=213,y=71

Answer 2

By large pipe only it will take 319.5 hours to fill the pool.

Explanation:

Let r₁ be the rate of filling of small pipe, r₂ be the rate of filling of large pipe and V be the volume of swimming pool.

`\texttt{Rate of small pipe},r_1=(V)/(t_1)\\\\\texttt{Rate of large pipe},r_2=(V)/(t_2)=(V)/(0.5t_1)=2r_1`

If both pipes are combined it takes 213 hours, that is

`t=(V)/(r_1+r_2)\\\\213=(V)/(r_1+2r_1)\\\\V=639r_1`

Now we need to find how much time it takes to fill the pool by large pipe,

That is

`t_2=(V)/(r_2)=(639r_1)/(2r_1)=319.5hours`

By large pipe only it will take 319.5 hours to fill the pool.