Respuesta :
Answer:
60 minutes.
Step-by-step explanation:
Let t represent time taken by larger hose in minutes to fill the pool.
Part of pool filled by larger hose in one minute would be [tex]\frac{1}{t}[/tex].
We have been given that it takes a smaller hose 3 times as long to fill a small swimming pool as it does a larger hose, so smaller hose will take [tex]3t[/tex] minutes to fill the pool.
Part of pool filled by smaller hose in one minute would be [tex]\frac{1}{3t}[/tex].
We are also told that it takes both hoses working together 15 minutes to fill the swimming pool, so part of pool filled by both hoses in one minute would be [tex]\frac{1}{15}[/tex].
[tex]\frac{1}{t}+\frac{1}{3t}=\frac{1}{15}[/tex]
[tex]\frac{1}{t}\cdot 15t+\frac{1}{3t}\cdot 15t=\frac{1}{15}\cdot 15t[/tex]
[tex]15+5=t[/tex]
[tex]t=20[/tex]
So it will take 20 minutes for the larger hose to fill the pool alone.
Since smaller hose takes 3 times as long to fill a pool, so 3 times 20 would be 60.
Therefore, it will take 60 minutes for the smaller hose to fill the pool alone.
Answer:
60 minutes
Step-by-step explanation:
Let the Larger hose take time to fill the swimming pool= x minutes
Than, time taken by smaller tank to fill the same swimming full tank= 3 x minutes
If both hoses work together time taken by both of them= 15 minutes
A.T.Q
[tex]\frac{1}{x}[/tex] +[tex]\frac{1}{3x}[/tex] = [tex]\frac{1}{15}[/tex]
[tex]\frac{3+1}{3x}[/tex] =[tex]\frac{1}{15}[/tex]
[tex]\frac{4}{3x}[/tex]= [tex]\frac{1}{15}[/tex]
x= [tex]\frac{15}{3}[/tex]× 4
x= 20 minutes
Larger hose take time to fill the swimming pool= 20 minutes
Than, time taken by smaller tank to fill the same swimming full tank= 3 x = =3× 20= 60 minutes
Hence. the correct answer is 60 minutes
