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Working together at their respective rates

This topic has 3 expert replies and 0 member replies

Working together at their respective rates

Post Thu Sep 21, 2017 6:32 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Working together at their respective rates, two hoses fill a pool in 2 hours. If one of the hoses, working alone, could fill the pool in 3 hours, how long would it take the other hose to fill the pool alone?

    A. 2 hours
    B. 3 hours
    C. 4 hours
    D. 5 hours
    E. 6 hours

    How will i formulate a formula here? Need experts advice. Thanks

    OAE

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    Post Thu Sep 21, 2017 7:43 pm
    Hi lheiannie07,

    This question is a standard example of a Work Formula question (with 2 'entities' working on a job together). When this type of question has no 'quirks' to it (such as 3 or more entities or one of the entities stops working partway through the job), you can use the Work Formula to answer it:

    Work = (A)(B)/(A+B) = amount of time to complete the job while working together (where A and B are the two individual times it takes to do the job).

    In this prompt, we know that one of the hoses takes 3 hours to do the job alone and that the two hoses (working together) can complete the job in 2 hours....

    (3)(B)/(3+B) = 2 hours
    3B = (2)(3+B)
    3B = 6 + 2B
    B = 6 hours

    Thus, it would take the second hose 6 hours to fill the pool by itself.

    Final Answer: E

    GMAT assassins aren't born, they're made,
    Rich

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    Post Fri Sep 22, 2017 6:24 am
    lheiannie07 wrote:
    Working together at their respective rates, two hoses fill a pool in 2 hours. If one of the hoses, working alone, could fill the pool in 3 hours, how long would it take the other hose to fill the pool alone?

    A. 2 hours
    B. 3 hours
    C. 4 hours
    D. 5 hours
    E. 6 hours
    Another approach is to assign a nice value to the job.
    In this case, we need a value that works well with the given information (2 hours and 3 hours).
    So, let's say the job consists of filling a pool containing 6 liters of water

    One of the hoses, working alone, takes 3 hours to fill the pool
    We'll call this hose A.
    Let A = the rate of work of this hose
    If it takes 3 hours for this hose to fill a 6-liter pool, then....
    A = 6/3 = 2 liters per hour (since rate = output/time)

    Working together at their respective rates, two hoses fill a pool in 2 hours.
    Let B = the rate of work of the other hose
    So, the COMBINED rate = A+B
    If it takes 2 hours for the combined hoses to fill a 6-liter pool then....
    A+B = 6/2 = 3 liters per hour (since rate = output/time)

    So, if A = 2 liters per hour, and A+B = 3 liters per hour
    Then we can see that B = 1 liter per hour

    How long would it take the other hose (hose B) to fill the pool alone?
    Time = output/rate = 6/1 = 6 hours

    Answer: E

    Cheers,
    Brent

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    Post Mon Sep 25, 2017 3:33 pm
    lheiannie07 wrote:
    Working together at their respective rates, two hoses fill a pool in 2 hours. If one of the hoses, working alone, could fill the pool in 3 hours, how long would it take the other hose to fill the pool alone?

    A. 2 hours
    B. 3 hours
    C. 4 hours
    D. 5 hours
    E. 6 hours
    We can let n = the time, in hours, it takes the other hose to fill the pool alone. Thus, the rate of that hose = 1/n. Since the rate of the known hose = 1/3 and the combined rate = 1/2, we have:

    1/n + 1/3 = 1/2

    Multiplying by 6n, we have:

    6 + 2n = 3n

    6 = n

    Thus, the other hose takes 6 hours to fill the pool.

    Answer: E

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