Mr. A and Mr. B worked on a project for 42 hours. Mr. A worked three times longer than Mr. B. how long did Mr. B work on the project?

2 Answers

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  • 5 months ago

    The answer is that Mr B worked 10.5 hours.

    Here's how you get this answer.

    Working step by step, find a way to express the times worked by each man.

    In this case, it is easiest to begin with the number of hours worked by Mr B.

    Let b equal the number of hours worked by Mr B.

    b <-- the number of hours worked by Mr. B

    Three times longer than that = 3b <-- the number of hours worked by Mr A

    Together these amounts add up to 42 hours total

    | Mr B's hours | plus | Mr A's hours | equals | the total number of hours

    | . . . . .b . . . . .| . .+ . | . . . . .3b . . . .| . . = . . | . . . . . . 42

    b + 3b = 42

    Solve for b, already defined as "the number of hours worked by Mr B"

    1) Combine like terms

    4b = 42

    2) Divide both sides by 4 to isolate b, already defined as "the number of hours worked by Mr B

    b = 10.5 <-- the number of hours worked by Mr B

    Three times more than that

    31.5 <-- the number of hours worked by Mr A

    Answer:Mr B worded 10.5 hours

    CHECK

    Mr B's hours . . 10.5

    Mr A's hours . . 31.5

    ------------------------------

    Total hours . . . .42.0

    Check

  • roger
    Lv 7
    5 months ago

    A + B  =42

    A+3A=42

    4A=42

    A=10.5

    B=31.5

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