Problema Solution
A pilot can travel 396 miles with the wind in the same amount of time as 324 miles against the wind. Find the pilot's speed in still air is 210 miles per hour.
Answer provided by our tutors
I will assume that what we need to find is the rate of the wind.
let
v = 210 mph the rate of the plane in still air
w = the rate of the wind
d1 = 396 mi the distance flying with the wind
d2 = 324 mi the distance flying against the wind
t = the time of each flight
since the rate = distance/time we have
when flying with the wind, the rate is: v + w
v + w = d1/t
210 + w = 396/t
t = 396/(210 + w)
when flying against the wind, the rate is: v - w
v - w = d2/t
210 - w = 324/t
t = 324/(210 - w)
that is we have:
396/(210 + w) = 324/(210 - w) cross-multiply
396(210 - w) = 324(210 + w)
by solving we find:
w = 21 mph
click here to see the step by step solution of the equation:
the rate of the wind is 21 mph.