SOLUTION: A turboprop plane flying with the wind flew 1,400 mi in 5 h. Flying against the wind, the plane required 7 h to travel the same distance. Find the rate of the wind and the rate of

Question 332548: A turboprop plane flying with the wind flew 1,400 mi in 5 h. Flying against the wind, the plane required 7 h to travel the same distance. Find the rate of the wind and the rate of the plane in calm air.
Answer by galactus(183) (Show Source): You can put this solution on YOUR website!
With the wind, we add the two rates. Against the wind, we subtract them.
Let rp=rate of plane and rw = the rate of thr wind.
With the wind:
Since d=rt, we have 1400=5(rp+rw)
Against the wind:
we have 1400=7(rp-rw)
These reduce to
rp+rw=280
rp-rw=200
Now, from the first equation we have rp=280-rw
Sub into the second equation:
280-rw-rw=200
280-2rw=200
rw=40=rate of wind.
That means the rate of the plane, rp, is 240.

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