SOLUTION: Please help me with this problem. I was never good with word problems. Please show all steps. A man flies a small airplane from Fargo to Bismarck, North Dakota --- a distance of

Question 1001626: Please help me with this problem. I was never good with word problems. Please show all steps.
A man flies a small airplane from Fargo to Bismarck, North Dakota --- a distance of 180 miles. Because he is flying into a head wind, the trip takes him 2 hours. On the way back, the wind is still blowing at the same speed, so the return trip takes only 1 hour 12 minutes. What is his speed in still air, and how fast is the wind blowing?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x = speed of the plane
let y = speed of the wind.

rate * time = distance.

when going against the wind, you subtract the wind speed from the plane speed.
when going with the wind, you add the wind speed to the plane speed.

distance = 180.

going against the wind, the formula becomes (x-y)*2 = 180

2 is the time and 180 is the distance.

coming back with the wind, the formula becomes (x+y)*1.2 = 180

1.2 is the time and 180 is the distance.

1.2 hours is the same as 1 hours and 12 minutes, because 12 minutes / 60 minutes in an hour = .2 hours.

you have 2 formulas that need to solved simultaneously, meaning that the same solution has to satisfy both equations.

the 2 equations are:

(x-y)*2 = 180
(x+y)*1.2 = 180

you solve these like you solve any 2 equations that have to be solved simultaneously.

one method i use is to just subtrct the second equation from the first after removing parentheses.

you will get:

2x - 2y = 180
subtract 1.2x + 1.2y = 180 from that to get:
2x - 1.2x = .8x
-2y - 1.2y = -3.2y
180 - 180 = 0
the result becomes:
.8x - 3.2y = 0
add 3.2y to both sides of this euation to get:
.8x = 3.2y
divide both sides of this equation by .8 to get:
x = 3.2y / .8 = 4y

since x = 4y, you can substitute 4y for x in either equation and then solve for y.

using the first equation:
2x - 2y = 180 becomes:
2*(4y) - 2y = 180 which becomes:
8y - 2y = 180 which becomes:
6y = 180

solve for y to get y = 30.

now that you know y, you can solve for x.
you will get x = 120.

the plane speed is 120 and the winds speed = 30.

from the first equation:
2*120 - 2*30 = 180 becomesw 240 - 60 = 180 which is true.

frm the second equation:
1.2*120 + 1.2*30 = 180 becomes 144 + 36 = 180 which is also true.

the solution is confirmed as good.

plane speed is 120 miles per hour.
wind speed is 30 miles per hour.

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