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Flying with a tailwind a plane averaged 158 km/h. On the return trip the plane averaged 112 km/h with same wind. Find wind & plane speed in still air.

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2 Answers

You need to name variables for plane speed and wind speed.  For example, I will name them:

x = Plane speed

y = Wind speed

Now you can create two equations in two variables

x + y = 158

x - y =112

This is a good problem for elimination method since you already have one equation with positive y and the other with negative y

x + y = 158
x - y = 112
2x    = 270

x = 135

Now substitute the value into either equation to solve for y

x + y - 158

135 + y = 158

y = 23

 

Hi Roxi -- here's another angle: during a round trip, the wind effect cancels out, much like going downhill and returning uphill. Your "still air" speed would be the average for the round trip = (158+112)/2= 135mph. Therefore, a 23-mph wind boosted the plane to 158 and slowed it to 112.  Best regards ma'am ...

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I used this method on another problem and I'm getting two different answers.

A small jet plane whose speed in still air is 220 km/h can travel 520 km with the wind in the same amount of time as it takes to fly 360 km against the wind. What is the wind speed?

I get (220+ 360)/2 = 70. But if I use John's method.

I get wind speed is 80.

220t +w = 520 and 220t -2 = 360. Using elimination method I get 440t =880

t=2. Then substitute into eq 1 and get 220(2) +w = 520 2 = 80

So which is right?

Wind speed is 40 km/h; total trip time 880 km/ 220 km/h=  4hours.

2 hours each leg==> 520/2= 260 km/h with 40 wind boost; 360/2= 180 km/h against same wind of 40 :) 

Wind speed is 40 km/h; total trip time 880 km/ 220 km/h=  4hours.

2 hours each leg==> 520/2= 260 km/h with 40 wind boost; 360/2= 180 km/h against same wind of 40 :) 

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