Algebra 2 word problem

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just checking to see if i have this problem correct

Sammy can cut wood twice as fast as Joe. When they both work together, it takes them 4 hrs. how long would it take them to do the job alone?

4/x +4/x+2 = x^2+2

4x+4x+8= x^2+2
8x+8= x^2+2

x^2-6x-8=0

(x-4)(x+2)
x=4 x=-2 since i can't use a -2 i have to put in a 4

x+2=4+2=6

Sammy =6 hours
6x2=12
Joe = 12 hours

Thanks

  • Algebra 2 word problem -

    Joe's rate ---- 1/2x
    Sammy's rate --- 1/x
    combined rate = 1/x + 1/2x = 3/(2x)

    time to do job with combined rate = 1/(3/(2x)) = 2x/3
    but we know that is 4 hrs
    2x/3 = 4
    2x=12
    x = 6 and then 2x = 12

    So Sammy could do it 6 hours
    and Joe would take 12 hours.

  • Algebra 2 word problem -

    BTW, I won't even begin to point out all the errors in your solution.
    Your opening equation makes no sense, and has no relation to the question.
    the 2nd line does not follow from the 1st line
    your "solution" of x=4 does not even satisfy your opening equation , as it should.

    It looks like you knew what the answer was supposed to be, and simply formed some expression that contain that answer.

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