# An airplane took 4 hours to fly 1200 miles against a headwind. The return trip with the wind took 3 hours. Find the speed of the plane in still air and the speed of the wind?

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word problem

word problem

##### 1 Answer

Oct 10, 2017

Start with the formula

#### Explanation:

...distance = rate x time.

from that, you can calculate the rate, given distance and time.

You have a rate r1 for the upwind trip, and r2 for the downwind trip.

Let the plane's still-air speed be

So, from the above, for the upwind trip, the plane travels at its still-air speed MINUS the wind speed, so:

For the downwind trip, the plane travels at velocity:

...Whaddaya know, we got 2 equations and 2 unknowns, so we can solve & find them. Start by adding the two equations:

or:

p = 350

w = 50

GOOD LUCK!