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Math Help - Current~ (Word Problem)

  1. #1
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    Current~ (Word Problem)

    A stream has a current of 4mph. Find the speed of Joe's boat in still water if it goes 40mph downstream in the same time it takes to go 24 miles upstream.

    I think I solved this correctly but I would like a second opinion/verification.

    -------------------------D----- R ------ T
    UP---------------------24---- 4-x
    DOWN -----------------40 --- 4+x

    so 24/4-x = 40/4+x
    96+24x=160-40x
    24x=64-40x
    64x=64
    x=1?

    Something about this problem seems off, but I'm not sure... any tips or verification would be nice.
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by Beastkun View Post
    A stream has a current of 4mph. Find the speed of Joe's boat in still water if it goes 40mph downstream in the same time it takes to go 24 miles upstream.

    I think I solved this correctly but I would like a second opinion/verification.

    -------------------------D----- R ------ T
    UP---------------------24---- 4-x
    DOWN -----------------40 --- 4+x

    so 24/4-x = 40/4+x
    96+24x=160-40x
    24x=64-40x
    64x=64
    x=1?

    Something about this problem seems off, but I'm not sure... any tips or verification would be nice.
    You have one small error. The speed of the boat up stream is

    x-4 \text{ not } 4-x

    This gives the equaiton

    \frac{24}{x-4}=\frac{40}{x+4}

    This will change the solution a bit.
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  3. #3
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    How can a boat go downstream with a helping current of 4mph unless its still water rate is 36mph
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  4. #4
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    Quote Originally Posted by bjhopper View Post
    How can a boat go downstream with a helping current of 4mph unless its still water rate is 36mph
    If you are getting 36 mph = 40 mph - 4 mph the 40 mph in the problem is a typo. It should be 40 miles. The boat is going x + 4 mph downstream and x - 4 mph upstream.

    -Dan
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  5. #5
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    Dear Dan,

    My statement is a wake up call to the OP and first responder. The upstream rate is 32 mph and the time to travel 24 mi is 3/4 hr. It makes no difference how far the boat goes downstream



    bjh
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  6. #6
    Behold, the power of SARDINES!
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    Quote Originally Posted by bjhopper View Post
    Dear Dan,

    My statement is a wake up call to the OP and first responder. The upstream rate is 32 mph and the time to travel 24 mi is 3/4 hr. It makes no difference how far the boat goes downstream

    bjh
    Dear bhhopper:
    I interpreted it as a typo because the problem is trivial if you already know the speed. This is standard problem in most algebra texts. Notice the table in the OP, this is used in many text books. We could ask Beastkun to clarify. The correct information is in the table!
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  7. #7
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    Quote Originally Posted by Beastkun View Post
    A stream has a current of 4mph. Find the speed of Joe's boat in still water if it goes 40mph downstream in the same time it takes to go 24 miles upstream.
    Well, clearly a typo: 40 mph should be 40 miles.
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