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?

Question

word problem

8760 views around the world

You can reuse this answer
Creative Commons License

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!