Problema Solution
It took an airplane 4 hours to fly 1760 miles against a headwind. The return trip with the wind took 3 2/3 hours. Find the speed of the plane with no wind and the windspeed.
Answer provided by our tutors
let
v = the speed of the plane in calm air, v>0
w = the wind speed, w>0
t1 = 4 hr the time of he travel against the wind
d = 1760 mi the distance flying in one direction
t2 = 3 2/3 = 11/3 hr the time of the return trip with the wind
the speed of the plane flying against the wind is: v - w
the speed of the plane flying with the wind is: v + w
since speed = distance/time we have
v - w = d/t1
v - w = 1760/4
v - w = 440
v + w = d/t2
v + w = 1760/(11/3)
v + w = 480
by solving the system of equations
v - w = 440
v + w = 480
we find
v = 460 mph
w = 20 mph
click here to see the step by step solution of the system of equations
the speed of the plane with no wind is 460 mph.
the wind speed is 20 mph.