Problema Solution
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 provided by our tutors
Let
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
........
click here to see the system of equations solved for v and c
........
v = 140 mph
c = 20 mph
The headwind is 20 mph.
The speed of the plane in still air is 140 mph.