# 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?

## word problem

Oct 10, 2017

Start with the formula $d = r t$

#### Explanation:

...distance = rate x time.

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

$r = \frac{d}{t}$

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

$r 1 = \frac{1200}{4} = 300$ miles/hour.

$r 2 = \frac{1200}{3} = 400$ miles/hour.

Let the plane's still-air speed be $p$, and the wind speed be w.

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

$p - w = 300$

For the downwind trip, the plane travels at velocity:

$p + w = 400$

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

$p - w + p + w = 300 + 400$

or:

$2 p = 700$

p = 350

w = 50

GOOD LUCK!