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Posted by **Kian** on Monday, August 27, 2012 at 8:40am.

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**, Monday, August 27, 2012 at 8:59am1.

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 -
**Kian**, Monday, August 27, 2012 at 9:05amhow 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 -
**Reiny**, Monday, August 27, 2012 at 9:16amWell, 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 -
**Kian**, Monday, August 27, 2012 at 9:26amoh 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**, Monday, August 27, 2012 at 9:34amAs 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 -
**Kian**, Monday, August 27, 2012 at 9:50amoh 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 -
**Reiny**, Monday, August 27, 2012 at 9:59amThat's what I said.

Btw, look up there , you have x = 155

- MATH -
**Kian**, Monday, August 27, 2012 at 10:09amWell, 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..?