Need ASAP- linear systems?

Question

1.An aircraft travels 5432 km from montreal to paris in 7 h and returns in 8 h. the wind speed is constant. determine the wind speed and the speed of the aircraft in still air.

2.a patrol plane can carry fuel for 8 h flying time, and can fly at 300 km/h in still air. Its outbound patrol is against a 30 km/h head wind. it returns with a 30 km/h tailwind. how far can it fly against the head wind and return safely?

Answer 1

I'll go ahead and set up equations for you.

1.
Let x be the speed of the plane.
Let y be the wind speed.

7*(x+y)=5432
8*(x-y)=5432


2.
Let x be the distance flown.
Let y be the time flown on the way out.
Then (8-y) is the time flown on the way back.

y*(300+30) = x
(8-y)*(300-30) = x


You should be able to solve the problems from there :-)

Answer 2

These are based on the distance = rate x time formula. The speed of the plane is affected by the windspeed, so if there is a headwind the windspeed is subtracted from the plane's speed. If there's a tailwind it's added
1. Let p = plane speed and w = wind speed. I assume that the plane's trip is faster with a tailwind.
7(p+w) = 5432
8(p-w) = 5432

Do distributive property on both equations and use elimination method to solve. Or divide the first equation by 7 first and the second equation by 8 to get rid of the coefficients. Then do elimination method.

Answer 3

1. a=aircraft speed, w=wind speed
5432 = (a+w) * 7,
5432 = (a-w) * 8
so a=727.5, w=48.5

2. d = 1-way distance; t1=outbound time; t2=inbound time
d = 270*t1
d = 330*t2
t1+t2 = 8

eliminating d from the first 2 equations gives t1 = 11/9*t2
Then combining with the last equation gives,
t1 = 4.4; t2=3.6

Answer 4

http://en.wikipedia.org/wiki/Linear_Algebra