algebra

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A cruise ship is traveling in the Atlantic Ocean at a constant rate of 40 mi/h and is traveling 2 mi east for every 5 mi north. An oil tanker is 350 mi due north of the cruise ship and is traveling 1 mi east for every 1 mi south. a. How far is each ship from the point at which their paths cross? b. What rate of speed for the oil tanker woul put it on a collision course with the cruise ship?

  • algebra -

    For the path-crossing point, you don't need velocities. Let Y be miles north and X = miles east. Let (0,0) be the coordinates of the cruise ship initially.
    Y = 350 - X (for tanker)
    Y = (5/2) X (for cruise ship)
    The cross when
    0 = 350 - (7/2)X
    X = 100 miles
    Y = 250 miles
    a) The cruise ship is sqrt [(100)^2 + (250)^2] = 269.3 miles from that point initially. The tanker is
    sqrt [(100)^2 + (100)^2] = 141.4 miles away.

    b) First calculate when the cruise ship arrives at the crossing point, based upon its known speed:
    T = 269.3/40 = 6.73 hours

    Then calculate the speed that would put the tanker at that point at that time

    V = 141.4 miles/T

  • algebra -

    B is about 21 mi/h

    T = 269.3/40 = 6.73 hours
    the you have to 141.4/6.73 which equals 21 mi/h

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