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 15 minu

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 15 minutes to fill the swimming pool. How long will it take the smaller hose to fill the pool by itself?

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Savannah 2 months 2021-09-28T18:37:19+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-09-28T18:38:29+00:00

    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 \frac{1}{t}.

    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 3t minutes to fill the pool.

    Part of pool filled by smaller hose in one minute would be \frac{1}{3t}.

    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 \frac{1}{15}.

    \frac{1}{t}+\frac{1}{3t}=\frac{1}{15}

    \frac{1}{t}\cdot 15t+\frac{1}{3t}\cdot 15t=\frac{1}{15}\cdot 15t

    15+5=t

    t=20

    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.

    0
    2021-09-28T18:38:45+00:00

    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

    \frac{1}{x} +\frac{1}{3x} = \frac{1}{15}

    \frac{3+1}{3x} =\frac{1}{15}

    \frac{4}{3x}= \frac{1}{15}

    x= \frac{15}{3}× 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

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