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Work Problems with Quadratic Equations Help (page 2)

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By — McGraw-Hill Professional
Updated on Sep 27, 2011

Solutions

  1. Let t represent the number of minutes Alex needs to peel the potatoes. Tina needs t + 5 minutes to complete the job alone.

    Worker

    Quantity

    Rate

    Time

    Alex

    1

    Work Problems Solutions

    t

    Tina

    1

    Work Problems Solutions

    t + 5

    Together

    1

    Work Problems Solutions

    6

    The equation to solve is Work Problems Solutions . The LCD is 6 t ( t + 5).

    Work Problems Solutions

    Alex can peel the potatoes in 10 minutes and Tina can peel them in 10 + 5 = 15 minutes.

  2. Let t represent the number of minutes Jared needs to wash the car by himself. The time Rachel needs to wash the car by herself is t + 24.

    Worker

    Quantity

    Rate

    Time

    Jared

    1

    Work Problems Solutions

    t

    Rachel

    1

    Work Problems Solutions

    t + 24

    Together

    1

    Work Problems Solutions

    16

    The equation to solve is Work Problems Solutions . The LCD is 16 t ( t + 24).

    Work Problems Solutions

    Jared needs 24 minutes to wash the car alone and Rachel needs 24 + 24 = 48 minutes.

  3. Let t represent the number of hours Printing Press II needs to print the run by itself. Because Printing Press I needs five fewer hours than Printing Press II, t – 5 represents the number of hours Printing Press I needs to complete the run by itself.

    Worker

    Quantity

    Rate

    Time

    Press I

    1

    Work Problems Solutions

    t − 5

    Press II

    1

    Work Problems Solutions

    t

    Together

    1

    Work Problems Solutions

    6

    The equation to solve is Work Problems Solutions . The LCD is 6 t ( t – 5).

    Work Problems Solutions

    Printing Press II can print the run alone in 15 hours and Printing Press I needs 15 – 5 = 10 hours.

  4. Let t represent the number of hours Pipe II needs to fill the reservoir alone. Pipe I needs one hour forty minutes less to do the job, so Work Problems Solutions represents the time Pipe I needs to fill the reservoir by itself.

    Worker

    Quantity

    Rate

    Time

    Pipe I

    1

    Work Problems Solutions

    Work Problems Solutions

    Pipe II

    1

    Work Problems Solutions

    t

    Together

    1

    Work Problems Solutions

    2

    The equation to solve is Work Problems Solutions . The LCD is Work Problems Solutions .

    Work Problems Solutions

    ( Work Problems Solutions cannot be a solution because Work Problems Solutions would be negative)

    Pipe II can fill the reservoir in 5 hours and Pipe I can fill it in Work Problems Solutions hours or 3 hours 20 minutes.

  5. Let t represent the number of hours Gary needs to unload the truck by himself. John needs 36 minutes more than Gary needs to unload the truck by himself, so John needs Work Problems Solutions more hours or Work Problems Solutions more hours. The number of hours John needs to unload the truck by himself is Work Problems Solutions .

    Together they can unload the truck in 1 hour 20 minutes, which is Work Problems Solutions hours. This means that the Together rate is Work Problems Solutions Work Problems Solutions .

    Worker

    Quantity

    Rate

    Time

    John

    1

    Work Problems Solutions

    Work Problems Solutions

    Gary

    1

    Work Problems Solutions

    t

    Together

    1

    Work Problems Solutions

    Work Problems Solutions

    The equation to solve is Work Problems Solutions. The LCD is Work Problems Solutions .

    Work Problems Solutions

    Gary needs Work Problems Solutions hours or 2 hours 24 minutes to unload the truck. John needs 2 hours 24 minutes + 36 minutes = 3 hours to unload the truck.

Practice problems for this concept can be found at: Algebra Quadratic Applications Practice Test.

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