Question

It takes a smaller hose
3
times as long to fill a small swimming pool as it does a larger hose. It takes both hoses working together
30
minutes to fill the swimming pool. How long will it take the smaller hose to fill the pool by itself?

Answer 1

let the larger hose take x min to fill the tank
then the smaller hose takes 3x min
let volume of the tank be V

so
rate of small pipe =V/3x galons/minute
rate of large pipe=V/x gallons/minute

rate together=v/3x + v/x

volume filled by the pipes in 30 min is V (whole tank)
thus
30(v/3x+v/x)=v

Answer 2

\(30 \times( \frac{v}{3x} + \frac{v}{x})=v\)

Answer 3

solve that, 'v' gets cancelled, it becomes an equation in one variable 'x'

Answer 4

Let a and b be the smaller and larger fill times respectively.
Solve the following for a and b:\[\left\{\frac{1}{a}+\frac{1}{b}=\frac{1}{30},\frac{b}{a}=3\right\} \]where 1/a means 1 filling per "a" minutes and so forth.
a = 40 minutes and b = 120 minutes.

Answer 5

@niz1995 did you understand it?

Answer 6

this is what I think about your question,

when both hoses fill the tank together, after 30 minutes, "1/4 of tank is filled by small tank"

Answer 7

so if small hose takes 30 minutes to fill 1/4th of the tank, It will take 4*30 minutes for the small hose to fill whole tank

answer is 120min