Question 1001626
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.