Math Word Problem ..........?

A boat is went 10km downstream in 2 hours. on the way back it took 4 hours to go 8km against the current. determine the boats average speed and the speed of the current

please show all steps thank you

4 Answers

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  • 9 years ago
    Favorite Answer

    speed x time = distance

    If we call the speed of the boat r and the speed of the current c then the speed going

    downstread is (r + c) and we have

    (r + c) 2 = 10

    Going upstream the current reduces the total speed and you have

    (r - c)4 = 8

    expanding these out we have

    2r + 2c = 10 and

    4r - 4c = 8 we can divide this 2nd equation by 2 on both sides to get

    2r - 2c = 4 and we solve by ellimination by adding the first equation to this

    2r + 2c = 10

    ----------------

    4r = 14

    so r = 14/4 = 7/2

    Knowing that we can get c. Plug r = 7/2 into

    2r + 2c = 10 to get

    7 + 2c = 10 then

    2c = 10 - 7 = 3 then

    c = 3/2

  • Anonymous
    9 years ago

    10/2 = 5km/hr

    8/4 = 2km/hr

    4 hours is 66% of the time, 2 hours is 33% of the time, so .33 * 5 + .66 * 2 = 2.89 km/hr is the average speed.

    Speed of the current:

    5-2 = 3 km/hr

  • Anonymous
    9 years ago

    Is the speed of the current not 1.5..

    let x be the speed of the boat unchanged

    5km/h-xkm/h=2km/h+xkm/h

    3=2x

    x=1.5km/h

  • 4 years ago

    If something is 40% smaller, you merely subtract 40%. So 40% of 40 energy is sixteen: you are attempting this by utilising multiplying 40 by utilising 0.4. the respond could be 40 - sixteen = 24 A shorter way could merely be to multiply by utilising 40 by utilising 0.6, because's a million-0.4.

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