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Math Help - Distance application

  1. #1
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    Distance application

    Ship A leaves port sailing north at a speed of 25km/h. A half hour later, ship B leaves the same port sailing east at a speed of 20km/hr. Let t (in hours) be the time ship B has been at sea.
    a) find an expression in terms of t giving the distance between the two ships

    b) use the expression obtained in part a to find the distance between the two ships 2h after ship A has left port.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by lemontea View Post
    Ship A leaves port sailing north at a speed of 25km/h. A half hour later, ship B leaves the same port sailing east at a speed of 20km/hr. Let t (in hours) be the time ship B has been at sea.
    a) find an expression in terms of t giving the distance between the two ships

    b) use the expression obtained in part a to find the distance between the two ships 2h after ship A has left port.
    If ship B is traveling due east at a speed of 20\frac{km}{hr}, then the total distance traveled after t hours is 20t km. However, Ship A leaves a half hour before, traveling at a speed of 20\frac{km}{hr}. The distance traveled by Ship A would have to be 25(t+.5) km, since Ship A has been traveling a half hour longer that Ship B. When drawn, these two distances can be represented as legs of a triangle, with the hypotenuse being the distance between the ships. Thus, using the Pythagorean Theorem, we find that distance to be:

    D^2=(25(t+.5))^2+(20t)^2
    \longrightarrow D=\sqrt{(25(t+.5))^2+(20t)^2}

    Plug in 2 for t to find how far apart they are.

    Hope my explanation was clear!
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