MATH

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1. A boat traveled 210 miles downstream and back. The trip downstream took 10 hours, the trip back took 70 hours. What is the speed of the boat in still water? What is the speed of the current?

2. Flying to Kampala with a tailwind a plan averaged 158km/h. On the return trip, the plane only averaged 112 km/h while flying back into the same wind. Find the speed of the wind and the speed of the plane in still air.

  • MATH -

    1.
    speed of boat in still water --- x mph
    speed of current ---- y mph

    10(x+y) = 210 ----> x+y = 21
    70(x-y) = 210 ----> x-y = 3

    add them
    2x = 24
    x=12
    then y = 9

    speed of boat = 12mph , speed of current = 9 mph

    #2
    even easier ....
    define x and y as above

    x+y = 158
    x-y = 112
    etc

  • MATH -

    how come if I do:
    x+y=158
    x-y=112

    and then i subtract them:
    2y=46 -> y=23

    why do I get the speed of plane as 23?

  • MATH -

    Well, obviously the speed of the plane must be greater than the speed of the wind, so
    in x-y = 112
    x must be the plane's speed and y the wind's speed
    so sub y = 23 into
    x+y = 158
    x+23=158
    x = 155

  • MATH -

    oh okay
    thank you so much! i also have another question:
    does it matter whether we add or subtract simultaneous equations? do we have to either add or subtract or are both fine?

  • MATH -

    As long as you add and subtract the integers correctly, it does not matter.
    Remember that if we add two opposites we get zero
    and when we subtract two "likes" we also get zero

    so for your two equations
    x+y=158
    x-y=112

    if I add them ---> 2x = 270 , x = 135
    if I subtract ----> 2y = 46 , y = 23

    in general, if the signs are opposite, we add
    if the signs are the same, we subtract

    btw, how did you get 155 ????

  • MATH -

    oh okay thanks!
    I got 135 not 155...

    but does that apply everytime or is that just a shortcut type of thing? it's not wrong if I subtract x+y=158 and x-y=112 right?

  • MATH -

    That's what I said.
    Btw, look up there , you have x = 155

  • MATH -

    Well, obviously the speed of the plane must be greater than the speed of the wind, so
    in x-y = 112
    x must be the plane's speed and y the wind's speed
    so sub y = 23 into
    x+y = 158
    x+23=158
    x = 155

    ^that's what you said.. you wrote 155 not me..?

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