Problema Solution
A plane can travel 1,015 miles in 7 hours traveling against the wind. Traveling with the same wind, the plane can travel 820 miles in 4 hours. How fast can the plane travel in still air and how fast is the wind current?
Answer provided by our tutors
let
t1 = 4 hours is the time traveled with the wind
d1 = 1.015 miles the distance traveled against the wind in t1=7 hours
t2 = 7 hours is the time traveled against the wind
d2 = 820 miles the distance traveled with the wind in t2 = 4 hours
v = the speed of the plane in still air
w = the wind speed
the speed of the plane when traveling with the wind is: v + w
the speed of the plane when traveling against the wind is: v - w
since speed=distance/time => distance=speed*time
(v + w)*t1 = d1
(v - w)*t2 = d2
or if substitute the values for t1, t2, d1, d2 we get
(v + w) 7 = 1015 divide both sides by 7
v + w = 145
(v - w) 4 = 820 divide both sides by 4
v - w = 205
notice that
v + w = 145
v - w = 205
the speed against the wind is bigger then the speed with the wind thus we can conclude (and also confirm our conclusion by solving the system and finding w<0 ) that the plane is traveling with the speed of the wind 1,015 miles in 7 hours and against the wind 820 miles in 4 hours
by solving the system of equations
v + w = 145
v - w = 205
we find
v = 175 mph
w = - 30 mph
w<0 as we assumed.
click here to see the step by step solution of the system
the speed of the plane in still air is 175 mph while the speed of the wind is 30 mph.