Problema Solution
flying with the wind, a plane traveled 450 miles in 3 hrs. Flying against the wind, the plane traveled the same distance in 5 hrs. find the rate of the plane in calm air and the rate of the wind.
Answer provided by our tutors
With the wind, we add the two rates. Against the wind, we subtract them.
Let rp=rate of plane and rw = the rate of the wind.
With the wind:
Since d=rt, we have 450=(rp+rw)3
Against the wind:
we have 450=(rp-rw)5
These reduce to
rp+rw=450/3=150
rp-rw=450/5= 90
Adding the two equations, we get 2rp = 240
rp = 240/2 = 120
Putting the value of the determined value in the equations we get the value of rw.
rp+rw=150
120+rw=150
rw=150-120=30
So, rp=rate of plane=120 miles per hour and rw = the rate of the wind = 30 miles per hour