Problema Solution
Flying with the wind, a small plane flew 352 mi in 2 h. Flying against the wind, the plane could fly only 318 mi in the same amount of time. Find the rate of the plane in calm air and the rate of the wind.
Answer provided by our tutors
let
v = the rate of the plane in calm air
w = the rate of the wind
d1 = 352 mi the distance flying with the wind
t = 2 h the time of each flight
d2 = 318 mi the distance flying against the wind
since the rate = distance/time we have
when flying with the wind, the rate is: v + w
v + w = d1/t
v + w = 352/2
v + w = 176
when flying against the wind, the rate is: v - w
v - w = d2/t
v - w = 318/2
v - w = 159
by solving the system of equations:
v + w = 176
v - w = 159
we find:
v = 167.5 mph
w = 8.5 mph
click here to see the step by step solution of the system of equations:
the rate of the plane in calm air is 167.5 mph.
the rate of the wind is 8.5 mph.