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4 October, 02:25

Two teams of interns are wrapping donated gifts at a hospital. if the teams work alone, team a can wrap all of the gifts in 7 hours, and team b can wrap all of the gifts in 5 hours. how many hours will it take the interns to wrap all of the gifts if both teams work together? round the answer to the nearest half hour.

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  1. 4 October, 06:02
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    Together it would take 3 hours.

    Team A can wrap all gifts in 7 hours; thus they can wrap 1/7 of the gifts in 1 hour.

    Team B can wrap all gifts in 5 hours; thus they can wrap 1/5 of the gifts in 1 hour.

    1/7h + 1/5h = 1, where h is the number of hours; it equals 1 because it is 100% of the gifts;

    Find a common denominator. 35 is the first thing 7 and 5 will both divide into. Convert the fractions:

    5/35h + 7/35h = 1

    12/35h = 1

    Divide both sides by 12/35:

    12/35h : 12/35 = 1 : 12/35

    h = 1/1 : 12/35

    h = 1/1 * 35/12

    h = 35/12

    h = 2.9

    h ≈ 3
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