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Thread: 2x2 System word problem?

  1. #1
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    2x2 System word problem?

    An underwater(but near the surface) explosion is detected by sonar on a ship 30s before it is heard on deck. If sound travels at 5,000 ft/s in water and 1,000 ft/s in air, how far is the ship from the explosion?

    All I need is the equations and I'll be aright to go from their.
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  2. #2
    Senior Member topher0805's Avatar
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    Let $\displaystyle t$ be equal to the time it takes to be heard by the sonar.

    We then have that the time for it to be heard on deck is $\displaystyle t + 30$.

    $\displaystyle v = \frac {d}{t}$

    Therefore:

    $\displaystyle d = vt$

    And since the distances are equal:

    $\displaystyle 1000(t + 30) = 5000t$

    Now solve for $\displaystyle t$ to get:

    $\displaystyle 4000t = 30000$

    $\displaystyle t = 7.5$

    Now just plug that into the equation $\displaystyle d = vt$ to get:

    $\displaystyle d = 5000(7.5)$

    $\displaystyle d = 37,500$ feet
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