Question

A helicopter flies 168 miles against the wind in 2 hours; with the wind, it can fly 252 miles in the same amount of time. find the speed of the helicopter in still air.

Answer 1

V = speed of helicopter

v = speed of wind

V - v = speed of helicopter against the wind

d = distance traveled against the wind = 168 mi

t = time of travel = 2 h

using the equation

speed = distance/time

V - v = d/t

V - v = 168/2

V - v = 84

v = V - 84 eq-1

V + v = speed of helicopter with the wind

D = distance traveled with the wind = 252 mi

t = time of travel = 2 h

using the equation

speed = distance/time

V + v = D/t

V + v = 252/2

V + v = 126

using eq-1

V + V - 84 = 126

V = 105 mph

Answer 2

Let $v_h$ be the speed of the helicopter in still air. Let $v_w$ be the speed of the wind. Then, from the given information,

$(v_h-v_w)2=168\\ (v_h+v_w)2=252$

Adding the above 2 equations,

$4v_h=168+252\\ 4v_h=420\\ v_h=105$

The speed of the helicopter in still air $105 \;mi/hour$