Problema Solution
with a tail wind, a helicopter traveled 300 mi in 1 hour 40 min. The return trip against the same wind took 20 min longer. Find the wind speed and also the air speed of the helicopter.
Answer provided by our tutors
let
w = the wind speed
v = the air speed of the helicopter
d = 300 mi
t1 = 1 h 40 min = 1 40/60 h = 5/3 h
t2 = t1 + 20/60 = 5/3 + 1/3 = 2 h
the speed of the helicopter traveling with tale wind is: v + w
the speed of the helicopter traveling against the wind is: v - w
since speed=distance/time => distance = speed*time
with tale wind
(v + w)t1 = d
(v + w)(5/3) = 300
against the wind:
(v - w)t2 = d
(v - w)*2 = 300
by solving the system of equations
(v + w)(5/3) = 300
(v - w)*2 = 300
we find
v = 165 mph
w = 15 mph
click here to see the step by step solution of the system of equations
the wind speed is 15 mph.
the air speed of the helicopter is 165 mph.