3) With a headwind, a plane traveled 840 miles northward in 2 hours. With the same wind as a tail wind, the return trip took 1 hour and 45 mineutes. Find the plane's airspeed and the wind speed.
Note....1hr 45 min = 1.75 hrs
Let the speed of the plane in still air be S
Let the wind speed be W
Against the wind the plane's rate is (R - W) ....the wind slows the plane's normal speed
With the wind the plane's rate is (R + W).....the wind increases the plane's normal speed
So..... Rate * Time = Distance and we have that
(R -W) * 2 = 840 ⇒ 2R - 2W = 840 ⇒ R - W = 420 ⇒ R = 420 + W (1)
(R + W) *1.75 = 840 ⇒ 1.75 R + 1.75W = 840 (2)
Sub (1) into (2) for R and we have that
1.75(420 + W) + 1.75W = 840
735 + 1.75W + 1.75W = 840
735 + 3.5W = 840 subtract 735 from both sides
3.5W = 105 divide both sides by 3.5
W = 30 mph = wind speed
And using (1) the plane's speed is 420 + 30 = 450 mph