A plane traveled 240 miles. The trip was with the wind. It took 3 hours. The trip back was into the wind. The trip back took 6 hours. Find the speed of the plane in still air and the speed of the wind.

Lets suppose the speed of the plane in still air is s and speed of the wind is w and since speed in the formula below equals speed of the plane plus the wind's speed so speed=s+w for this journey with the wind

[tex]Speed=\frac{Distance}{Time}[/tex]

[tex]Distance=Speed*Time[/tex]

For the first journey the trip with the wind:

[tex]Distance=Speed*Time\\240=(s+w)(3)\\240/3=s+w\\s+w=80[/tex]

Here we got our first equation for the second equation we use the information from the second trip which was into the wind. Which means the speed here would be speed=s-w

[tex]Distance=Speed*Time\\240=(s-w)*6\\240/6=s-w\\s-w=40[/tex]

so now we got our two equations adding both equations would result into the following:

[tex]s+w=80\\s-w=40\\2s=120\\s=60[/tex]

so speed of the plane is 60 miles/hour put the value of s in any our two equations to calculate the wind speed, lets take the first equation:

[tex]s+w=80\\60+w=80\\w=80-60\\w=20[/tex]

so the wind speed is 20 miles/hour

A plane traveled 240 miles. The trip was with the wind. It took 3 hours. The trip back was into the wind. The trip back took 6 hours. Find the speed of the plane in still air and the speed of the wind.​

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A plane traveled 240 miles. The trip was with the wind. It took 3 hours. The trip back was into the wind. The trip back took 6 hours. Find the speed of the plane in still air and the speed of the wind.