A plane traveled 3575 miles with the wind in 6.5 hours and 3185 miles against the wind in the same amount of time. Find the speed of the plane in still air and the speed of the wind.

Answer 1

First list out your knowns and setup variables

Speed of plane with wind = S_WW

Speed of plane against the wind = S_AW

Speed of plane in still air = S_S

Speed of the wind = S_W

S_AW = S_S - S_W

S_WW = S_S + S_W

Distance = Speed * time

Next, discover the values of S_AW & S_WW

3185 Miles = S_AW * 6.5 hours

S_AW = 3185 miles / 6.5 hours = 490 miles / hour

3575 Miles = S_WW * 6.5 hours

S_WW = 3575 miles / 6.5 hours = 550 miles / hour

Next, use one of the equations to solve for S_S

S_AW = S_S - S_W

S_AW + S_W = S_S

Next, plug the value of S_S into the other equation to solve for S_W

S_WW = S_S + S_W

S_WW = S_AW + S_W + S_W

(550 miles / hour) = (490 miles / hour) + 2*S_W

(60 miles / hour) = 2*S_W

(30 miles / hour) = S_{W <--- Answer}

Next, plug the value of S_W into one of the equations to solve for S_S

S_WW = S_S + S_W

(550 miles / hour) = S_S + (30 miles / hour)

(520 miles / hour) = S_{S <--- Answer}

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Always check your work

S_AW = S_S - S_W

490 = 520 - 30

490 = 490 CORRECT!

S_WW = S_S + S_W

550 = 520 + 30

550 = 550 CORRECT!

Answer 2

3575 = (R+S)*6.5 = 6.5R + 6.5S

3185 = (R-S)*6.5 = 6.5R - 6.5S

6760 = 13R

R=520

Per first equation: 3575 = 6.5*520 + 6.5S

3575 = 3380 + 6.5S

195 = 6.5S

S = 30

Speed of plane is 520

Speed of the wind is 30