Problema Solution
A plane traveled 416 miles to Tokyo and back. The trip there was with the wind. It took 4 hours. The trip back was into the wind. The trip back took 8 hours. Find the speed of tht plane in still air and the speed of the wind.
Answer provided by our tutors
let
d = 416 mi the distance traveled forth and back
t1 = 4 hr the time of the travel with the wind
t2 = 8 hr the time of the travel against the wind
v = the speed of the plane in still air
w = the speed of the wind
the speed = distance/time
traveling with the wind the speed of the plan is: v + w
v + w = (d/2)/t1
v + w = (416/2)/4
traveling against the wind the speed of the plane is: v - w
v - w = (d/2)/t2
v - w = (416/2)/8
by solving the system of equations:
v + w = (416/2)/4
v - w = (416/2)/8
we find:
v = 39 mph
w = 13 mph
click here to see the step by step solution og the system of equations:
the speed of the plane in still air is 39 mph.
the speed of the wind is 13 mph.