Asked by Kian

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.
Answered by Reiny
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
Answered by Kian
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?
Answered by Reiny
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
Answered by 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?
Answered by 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
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 ????
Answered by 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 x-y=112 right?
Answered by Reiny
That's what I said.
Btw, look up there , you have x = 155
Answered by Kian
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..?
Answered by Anonymous
why is 1 equation x+y and the other X-y
There are no AI answers yet. The ability to request AI answers is coming soon!