SOLUTION: A plane makes a 240-mile trip against a head wind in 1 hour and 30 minutes and returns, with a tail wind of the same speed, in 1 hour. What is the speed of the wind and what is th

Question 172797: A plane makes a 240-mile trip against a head wind in 1 hour and 30 minutes and returns, with a tail wind of the same speed, in 1 hour. What is the speed of the wind and what is the speed of the plane?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let w=speed of wind and p=speed of plane

Note: 1 hour and 30 minutes = 1.5 hours (ie 1 and a half hours)

Against Wind:

Going against the wind will slow you down. So this means that the speeds plane against the wind is

Start with the distance rate time formula

Plug in , , and (this is the time it takes to go against the wind)

Divide both sides by

Divide.

Add "w" to both sides to isolate "p".

So after isolating "p", we get

--------------------------------------------------------------

With Wind:

In contrast, going with the wind will speed you up. So this means that the speeds plane with the wind is

Start with the distance rate time formula

Plug in , , and (this is the time it takes to go with the wind)

Multiply

Plug in

Subtract 160 from both sides.

Combine like terms.

Divide both sides by to isolate

Reduce

So the first answer is . This means that the speed of the wind is 40 mph

--------------------------------------------

Go back to the previously isolated equation

Plug in

Add

So the second answer is . This means that the speed of the plane is 200 mph

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Answer:

So the solutions are and

This means that the speed of the wind is 40 miles per hour and the speed of the plane is 200 miles per hour.

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