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Answer:
- Wind speed:
.
- Speed of the plane in still air:
.
Step-by-step explanation:
This problem involves two unknowns:
- wind speed, and
- speed of the plane in still air.
Let the speed of the wind be , and the speed of the plane in still air be
. It takes at least two equations to find the exact solutions to a system of two variables.
Information in this question gives two equations:
- It takes the plane three hours to travel
from Ottawa to with a tail wind (that is: at a ground speed of
.)
- It takes the plane four hours to travel
.)
Create a two-by-two system out of these two equations:
.
There can be many ways to solve this system. The approach below avoids multiplying large numbers as much as possible.
Note that this system is equivalent to
.
.
Either adding or subtracting the two equations will eliminate one of the variables. However, subtracting them gives only on the right-hand side. In comparison, adding them will give
, which is much more complex to evaluate. Subtracting the second equation (
) from the first (
) will give the equation
.
.
.
Substitute back into either equation
or
of the original system. Solve for
to obtain
.
In other words,
- Wind speed:
- Speed of the plane in still air: