need a little help solving distance problem?

Question

Flying with the wind, a plane takes 1hr to go from city A to city B. Flying against the wind, the plane takes 2hrs to go from city B to city A. The trip from A to B is 200 miles. What is the speed of the plane and the wind?
a = speed of plane, w = speed of plane

I've only been able to get this far..
(a+w)*1=200
(a-w)*2=200

a+w=200
2a-2w=200
I know I need to substitute the problems then plug that number back in to get the second answer, but how do I do it?

well if I'm doing something wrong, please let me know instead of being rude.

Answer 1

You have it right . . . solve for one variable and plug it into the other.

a = 200-w. So,

2(200-w) - 2w = 200
400-2w-2w = 200
400 - 4w = 200
400 - 200 = 4w
200 = 4w
50 = w. Then plug this back in to other equation:

a + 50 = 200
a = 150

So, a = 150 and w = 50

Answer 2

solve one of the equations for one of the variables and then plug it in. For the first equation, I'd solve it for a.... so.... a=200-w. Then plug (200-w) into the second equation in place of the a. So the equation would now be:
2(200-w) - 2w = 200
Then you should be able solve it. :)

Answer 3

So far so good.

a + w = 200
2a - 2w = 200

Solve the top one for one of the variables. (I'll pick a.)
a = 200 - w

Now, put that into the other equation.
2a - 2w = 200
2(200 - w) - 2w = 200
400 - 2w - 2w = 200
400 - 4w = 200
-4w = -200
w = 50

Now, put that back into one of the equations to find a.

Answer 4

you have solved almost
now a+w=200-----------------(1)
& 2a-2w=200------------------(2)
multiplying (1) with 2,we get
2a+2w=400--------------------(3),adding (2) & (3),we get
4a=600 or a=600/4=150,put this value in (1),we get 150+w=200 or w=200-150=50
so a(speed of plane)=150 miles & w(the speed of wind)=50 miles ans

Answer 5

I like to divide the 2nd equation by 2 to get this system:

a+w = 200
a-w = 100 .............. then add
--------------
2a = 300
a = 150

and if you subtract,

a+w = 200
-a+w = -100
------------------
2w = 100
w = 50

Answer 6

substituting:

a+w=200
a=200-w

2[200-w]-2w=200
400-2w-2w=200
4w=200
w=50

a=200-50=150

Answer 7

enable c be the canoeist's speed in nevertheless water, in miles according to hour. Downstream speed = c + a million Upstream speed = c - a million 24 minutes × a million hour/60 minutes = 0.4 hour Time to paddle 12.6 miles downstream = 12.6 miles × a million hour/(c + a million) miles = 12.6/(c + a million) hour Time to paddle 12.6 miles upstream = 12.6 miles × a million hour/(c - a million) miles = 12.6/(c - a million) hour 12.6/(c - a million) hour - 12.6/(c + a million) hour = 0.4 hour remedy for c

Answer 8

OBZu!+You+can+find+solution+here!