Question

I need help!!!!!!!!
An airplane flew 3 hours with a 40 mph head wind. The return trip with a tail wind of the same speed took 2 hours. Find the speed of the plane in still air.
-180 miles?
-200 miles?
-220 miles?
-240 miles?

Answer 1

Let v be the speed of the plane.
t1=3 hrs
t2=2 hrs

Answer 2

(v-40) t1= s miles
(v+40) t2=s miles

Now equate the two equations, substitute for t1 & t2 & find v.

Answer 3

(v-40) 3 = (v+40) 2
3v-120=2v+80
3v-2v=200
v=200mph

Answer 4

Call wind speed w and speed of the plane in still air v.
Head wind speed = v - w
Tail wind speed = v + w
Keep in mind that v > w. Otherwise, the plane will be flying "backward".
Since the distance is the same in both trips, we can write
(v - 40) x 3 = (v +40) x 2
3v - 120 = 2v + 80
v = 200 mph

Note: The answer should be 200 mph, not 200 miles.