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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Answer 1 · 2017-10-10T19:33:02

Start with the formula #d = rt#

...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!