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A boat traveled 45 miles downstream (w/ the current) in 3 hours and made the return trop (against the current) in 5 hours. What was the speed of the boat and what was the speed of the current?

  • math -

    b=boat (mph)
    c=current (mph)

    Set up equations using distance=speed*time
    3(b+c)=45 ...(1)
    5(b-c)=45 ...(2)

    Multiply (1) by 5 and (2) by 3:
    15b+15c = 225 ...(1a)
    15b-15c = 135 ...(2a)

    Add (1a) and (2a)
    30b+0 = 360
    b = 360/30 = 12

    Subtract (2a) from (1a)
    0+30c = 90
    c = 90/30 = 3

    Boat speed is 12 mph,
    current speed is 3 mph

  • math -

    speed of boat ---- x mph
    speed of current -- y mph

    then :
    1. 3(x+y) = 45 or x+y = 15
    2. 5(x-y) = 45 or x-y = 9

    add them:
    2x = 24
    x = 12

    from one of the others, y = 3

    etc.

  • math -

    thank you guys so much

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