Posted by Kian on .
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 
Reiny,
1.
speed of boat in still water  x mph
speed of current  y mph
10(x+y) = 210 > x+y = 21
70(xy) = 210 > xy = 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
xy = 112
etc 
MATH 
Kian,
how come if I do:
x+y=158
xy=112
and then i subtract them:
2y=46 > y=23
why do I get the speed of plane as 23? 
MATH 
Reiny,
Well, obviously the speed of the plane must be greater than the speed of the wind, so
in xy = 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 
Kian,
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 
Reiny,
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
xy=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 
Kian,
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 xy=112 right? 
MATH 
Reiny,
That's what I said.
Btw, look up there , you have x = 155 
MATH 
Kian,
Well, obviously the speed of the plane must be greater than the speed of the wind, so
in xy = 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..?