SOLUTION: Plane flies from Det. to Den. it has to fly against the wind and takes 8 hours. On return it goes with wind takes 7 hours. If distance between Det. and Den. is 1120 miles what as s

Question 913547: Plane flies from Det. to Den. it has to fly against the wind and takes 8 hours. On return it goes with wind takes 7 hours. If distance between Det. and Den. is 1120 miles what as speed of the airplane in still are ? What was speed of wind ?
1120=8p-8w
1120=7p+7w
p represents plane w wind I got this far and am confused since I
cant substitute ?
Found 3 solutions by josgarithmetic, mananth, MathTherapy:
Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!
p for speed of the PLANE if no wind
w for speed of wind entirely in one direction or the other direction

__________________rate__________time_________distance
DET to DEN________p-w____________8___________1120
DEN to DET________p+w____________7___________1120

The uniform rates travel rule is RT=D rate time distance. Your data give two linear equation in the variables p and w.
.
Solve the system.
This IS just as you have; which is two equation in two unknowns. YES, substitute! Do you prefer to use the elimination method? You can use that if you want instead.

My impression is that you are only temporarily stuck on nothing. You only believe you are stuck.
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
p= speed of plane in still air
w= speed of plane in still air wind

8 p -8 w = 1120 .............1

7 p + 7 w = 1120 .............2
Eliminate y
multiply (1)by 7
Multiply (2) by 8
56 p -56 w = 7840
56 p + 56 w = 8960
Add the two equations
112 p = 16800
/ 112
p = 150
plug value of p in (1)
8 p -8 w = 1120
1200 -8 w = 1120
-8 w = 1120 -1200
-8 w = -80
w = 10
p= 150 speed of plane in still air
w= 10 speed of wind
m.ananth@hotmail.ca

Answer by MathTherapy(10557)   (Show Source): You can put this solution on YOUR website!

Plane flies from Det. to Den. it has to fly against the wind and takes 8 hours. On return it goes with wind takes 7 hours. If distance between Det. and Den. is 1120 miles what as speed of the airplane in still are ? What was speed of wind ?
1120=8p-8w
1120=7p+7w
p represents plane w wind I got this far and am confused since I
cant substitute ?

Let speed of airplane in still air, be S, and wind, W
Then, "against the wind equation" is: _____ ----- eq (i)
"With the wind equation" is: ______________ ----- eq (ii)
2S = 300 ------ Adding eqs (i) & (ii)
S, or speed of airplane, in still air = , or mph
150 - W = 140 ------- Substituting 150 for S in eq (i)
- W = 140 - 150
- W = - 10
W, or speed of wind = , or mph
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