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# algebra... head and tail wind?

with a head wind a plane traveled 500 miles in 5 hours. with a tail wind the plane flew the return trip in 4 hours and 10 minutes. find the speed of the plane and the speed of the wind

### 3 Answers

- Pi R SquaredLv 71 decade agoFavorite Answer
Hi,

25/6(P + W) = 500

5(P - W) = 500

25/6(P + W) = 500

5P - 5W = 500

Multiply the first equation by 6 to eliminate the fraction. Multiply the second equation by -5. Add the equations and solve.

25(P + W) = 3000

5P - 5W = 500

25P + 25W = 3000

-5(5P - 5W = 500)

25P + 25W = 3000

-25P + 25W = -2500

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

50W = 200

W = 10

If W = 10 and 5(P - W) = 500, then:

5(P - 10) = 500

5P - 50 = 500

5P = 550

P = 110

The plane's speed is 110 mph and the wind's speed is 10mph. <==ANSWER

I hope that helps!! :-)

- Joel LLv 61 decade ago
First trip ground speed was 500 miles / 5 hours = 100 mi/hr

Return trip ground speed was 500 miles / 4 1/6 hours = 120 mi/hr

The air speed is 110 mi/hr and the wind speed is 10 mi/hr

- 1 decade ago
how would you solve it?

you have two trips.. each with a speed. If you average the two speeds, you have the speed of the plane, and the difference between the speed of each trip and the plane speed is the wind speed.