To model and solve our situation we are going to use the equation:
where
is speed
is distance
is time
1. We know that the distance between the cities is 2400 miles, so
. We also know that the speed of the plane is 450 mi/h. Since we don't know the speed of the air,
. We don't know how much the westward trip takes, so
, and we also don't know how much the eastward trip takes, so
.
Going westward. Here the plane is flying against the air, so we need to subtract the speed of the air from the speed of the plane:
Going eastward. Here the plane is flying with the the air, so we need to add the speed of the air to the speed of the plane:
2. We know for our problem that the round trip takes 11 hours; so the total time of the trip is 11,
. Notice that we also know that the total time of the trip equals time of the tip going westward plus time of the trip going eastward, so
. Since we know that the total trip takes 11 hours, we can replace that value in our total time equation and solve for
:
Now we can replace
in our going westward equation to model our round trip with a system of equations:
equation (1)
equation (2)
3. To solve our system of equations, we are going to solve for
in equations (1) (2):
From equation (1)
equation (3)
From equation (2):
equation (4)
Replacing (4) in (3)
Now, we can solve for
to find the speed of the wind:
Since speed cannot be negative, the solution of our equation is:
We can conclude that the speed of the wind is 78 mph.
