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

1 Answer
Oct 10, 2017

Start with the formula d = rt

Explanation:

...distance = rate x time.

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

r = d/t

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

r1 = 1200/4 = 300 miles/hour.

r2 = 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:

2p = 700

p = 350

w = 50

GOOD LUCK!