Problema Solution
In 2 1/2 hours an airplane travels 950km against the wind. It takes 50 min to travel 350km with the wind. Find the speed of the wind and the speed of the airplane still in the air.
Answer provided by our tutors
let
p = the plane's speed in still air
w = the speed of the wind
d1 = 950 km against the wind
t1 = 2 1/2 hours = 2.5 hour the time traveling against the wind
d2 = 350 km with the wind
t2 = 50 min = 50/60 hours = 5/6 hours the time traveling 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 = distance/time => distance = speed*time
d1 = (p - w)t1
950 = (p - w)2.5
(p - w)2.5 = 950 divide both sides by 2.5
p - w = 380
d2 = (p + w)t2
(p + w)(5/6) = 350 multiply both sides by 6/5
p + w = 420
by solving the system of equations
p - w = 380
p + w = 420
we find
p = 400 km/h
w = 20 km/h
click here to see the step by step solution of the equations
the speed of the plane in still air is 400 km/h.
the speed of the wind is 20 km/h.