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23 September, 11:43

Next-door neighbors Bob and Jim use hoses from both houses to fill Bob's swimming pool. They know that it takes 22 h using both hoses. They also know that Bob's hose, used alone, takes 50% less time than Jim's hose alone. How much time is required to fill the pool by each hose alone?

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  1. 23 September, 12:01
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    correct answer: Bob's hose required alone 33 hours and Jim's hose required alone 66 hours

    Step-by-step explanation:

    Given:

    Bob's hose time = 50% of Jim's hose time ⇒

    ⇒ Jim's hose time = 2 · Bob's hose time

    Let be x Bob's hose time and 2x Jim's hose time

    The following equation will solve the problem:

    1/x + 1 / 2x = 1/22

    The common denominator for both fractions is 2x, so we will multiply the first fraction by the number 2 and get:

    2/2x + 1/2x = 1/22 ⇒ 3/2x = 1/22 ⇒ x = 3 · 22 / 2 ⇒ x = 3 · 11 = 33 hours

    Bob's hose time x = 33 hours and

    Jim's hose time 2x = 66 hours

    God is with you!
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