Problema Solution
A jet travels 4912 miles against the wind in 8 hours and 6192 miles with the wind in the same amount of time. What is the rate of the jet in still air and what is the rate of the wind?
Answer provided by our tutors
let
p = the plane's speed (rate) in still air
w = the speed (rate) of the wind
d1 = 4912 miles against the wind
t = 8 hours the time traveling in one direction
d2 = 6192 miles with the wind
the speed of the plane traveling against the wind is: p - w
the speed of the plane traveling with the wind is: p + w
since speed (or rate) = distance/time => distance = speed*time
when traveling against the wind:
d1 = (p - w)t
(p - w)t = d1
(p - w)8 = 4912 divide both sides by 8
p - w = 614
when traveling with the wind
d2 = (p + w)t
(p + w)t = d2
(p + w)8 = 6192 divide both sides by 8
p + w = 774
by solving the system of equations
p - w = 614
p + w = 774
we find
p = 694 mph
w = 80 mph
click here to see the step by step solution of the system of equations
the rate of the jet in still air is 694 mph.
the rate of the wind is 80 mph.