Posted by Kian on Monday, August 27, 2012 at 8:40am.
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
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?
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
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?
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 ????
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?
That's what I said.
Btw, look up there , you have x = 155
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..?