An airplane traveled 1092 miles with a tailwind, turned around and returned 1092 miles against the same wind to its starting point. The trip with the wind took 6hrs and the return flight against the wind took 8hrs. Find the speed of the plane and the wind.
dealing w/- subst. and elimin.
let the speed of the plane in still air be x mph
let the speed of the wind by y mph
6(x+y) = 1092
8(x-y) = 1092
divide the first equation by 6, then second by 8, then add them
looks quite easy
To find the speed of the plane and the speed of the wind, we can use the concept of relative speed.
Let's assume that the speed of the plane is represented by "p" and the speed of the wind is represented by "w."
When the plane is flying with the wind, the effective speed of the plane will be increased by the speed of the wind. So the speed of the plane with the tailwind is given by (p + w).
Similarly, when the plane is flying against the wind, the effective speed of the plane will be decreased by the speed of the wind. So the speed of the plane against the wind is given by (p - w).
According to the given information:
Distance traveled with the wind = 1092 miles
Time taken with the wind = 6 hours
Using the formula: Speed = Distance / Time, we can write the equation:
(p + w) = 1092 / 6
Distance traveled against the wind = 1092 miles
Time taken against the wind = 8 hours
Similarly, we can write the equation:
(p - w) = 1092 / 8
Now, we have a system of equations:
(p + w) = 182
(p - w) = 136.5
To solve this system of equations, we can use the method of substitution or elimination.
Let's use the method of substitution:
From the first equation, we can express p in terms of w: p = 182 - w
Substituting this value of p in the second equation, we get:
(182 - w) - w = 136.5
Simplifying, we have:
182 - 2w = 136.5
Now, let's solve for w:
182 - 136.5 = 2w
45.5 = 2w
w = 45.5 / 2
w = 22.75 mph
Substituting the value of w back into the first equation, we can find p:
(p + 22.75) = 182
p = 182 - 22.75
p = 159.25 mph
So, the speed of the plane is 159.25 mph and the speed of the wind is 22.75 mph.