SOLUTION: Marcia flew her ultralight plane to a nearby town against a head wind of 15 km/h in 2 h and 20 minutes. The return trip under the same wind conditions took 1 h and 24 minutes. Find

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Question 646262: Marcia flew her ultralight plane to a nearby town against a head wind of 15 km/h in 2 h and 20 minutes. The return trip under the same wind conditions took 1 h and 24 minutes. Find the plane's air speed and the distance to the nearby town. I tried a chart and can't get it in the right order to solve. I have lots of wind problems on my homework assignment and just can't figure it out!
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Let represent the air speed and let represent the distance to the town. Also note that 20 minutes is one-third of an hour and 24 minutes is two-fifths of an hour.

We know that distance equals rate times time, so distance divided by rate must be time. When flying into the wind, ground speed will be air speed MINUS wind speed, hence the against the wind trip is described by:

And the downwind trip is then:

Cross-multiplying both we get the two-variable system:

This is easily solved by Elimination. Distribute the 7s across the parentheses. Multiply the first equation by -1. Add the two equations to eliminate the variable. Solve for . Once you have the value for substitute back into either equation and then solve for . Et Voil�!

John

My calculator said it, I believe it, that settles it