SOLUTION: A plane goes 150 miles with the wind and returns against the wind in 3 hours and 45minutes. Find the air speed if the plane if the wind blows 10mph.

Question 892313: A plane goes 150 miles with the wind and returns against the wind in 3 hours and 45minutes. Find the air speed if the plane if the wind blows 10mph.
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
SEE FARTHER BELOW FOR A MUCH BETTER SOLUTION PLAN!

r is speed without wind.

_____________________speed_________time___________distance
WITH_________________r+10__________x___________(r+10)x
AGAINST______________r-10__________y___________(r-10)y
Totals____________________________3&3/4_________150

SYSTEM FORMULATED INITIALLY
and

The way that the situation would become simpler to analyze is that the plane would travel equal distances with as against the wind. Exactly how is your given problem written? If equal distances in both directions,

_____________________speed_________time________distance
WITH_________________r+10__________x___________(r+10)x=d
AGAINST______________r-10__________y___________(r-10)y=d
Totals____________________________3&3/4_________150

And you can include .
You also say and which may allow elimination of r to solve for x and y.

rx+10x=75 and ry-10y=75;
rx=75-10x and ry=75+10y;
r=(75-10x)/x and r=(75+10y)/y;
Equate the expression of r;

Now recall earlier the equation .
Two equation in the unknowns x and y. Solve them and then use for finding r.

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The above shown solution method now seems overly complicated.
Assuming equal distance to and from, then each way is 75 miles.
RT=D allows us to make expressions for the time in each direction.

___________________speed_________time_________________distance
WITH_______________r+10__________75/(r+10)____________75
AGAINST____________r-10__________75/(r-10)____________75
Total____________________________3&3/4

Now only need to solve for r in .
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