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With a tailwind, a plane flew the from Calgary to Montreal in hours. The return flight, against the wind, took hours. Find the wind speed and the speed of the plane.
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Q. With a tailwind, a plane flew the from Calgary to Montreal in hours. The return flight, against the wind, took hours. Find the wind speed and the speed of the plane.
- Define speeds: Let's define the speed of the plane as km/h and the speed of the wind as km/h. The effective speed of the plane with the tailwind is km/h, and against the wind, it is km/h.
- Set up equations: Using the formula , we can set up the equations for the flights. For the flight from Calgary to Montreal, the equation is .
- Flight to Montreal: Simplifying the equation from the previous step, we get .
- Return flight: For the return flight against the wind, the equation is .
- Solve equations: Simplifying this equation, we get .
- Find speed: Now, we have two equations:. . We can solve these equations by adding them together.
- Substitute and solve: Adding the equations, we get . Solving for , we find .
- Substitute and solve: Adding the equations, we get . Solving for , we find . Substituting back into the equation , we solve for :
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