Christie pilots her plane for 240 mi against a headwind in 2 hrs. The flight would take 1 hr and 30 mins with a tailwind of the same speed. Find the headwind and the speed of the plane in still air.

Answer 1

240 = 2(r-c)

240 = 1.5(r+c)

2r-2c = 1.5r + 1.5c

.5r -= 3.5c

r= 7c

240 = 2(7c -c) = 2(6c) = 12c

240 = 12c

c = 240/12 = 20 mph = speed of the currewnt

r = 7c = 7(20) = 140 mph= speed of the plane in still air

240 in 2 hours against the wind is 2(140) = 280 - 2(20) = 240

240 in 1.5 hours = 1.5(140+20) = 1.5(160) = 240

Answer 2

v = the speed of the plane in still air

c = the speed of the headwind/tailwind

Since speed = distance/time we have:

when traveling with headwind the speed of the plane is v - c:

v - c = 240/2

v - c = 120

when traveling with tailwind the speed of the plane is v + c:

v + c = 240/1.5 (1 hour 30 min = 1.5 hours)

v + c = 160

We have the following system of equations:

v - c = 120

v + c = 160

when you solve them just add equations and c cancels out;

2v = 280, v = 140

140 +c =160

c= 20