Posted by Annie on Thursday, February 4, 2010 at 7:49pm.
Use systems of lineear equations to solve:
An airplane flew for 6 hours with a 22-km/h tail wind. The return flight against the same wind took 8 hours. Find the speed of the plane in still air.
I know the answer is 154 km/hr (back of book resources :) )...I just don't understand how you would get to that answer.
- Math - Anonymous, Thursday, February 4, 2010 at 10:37pm
Use the equation d = rt, once for each trip. I will use capitals for the variables and lowercase for subscripts.
D = R * T
Dr = Rr * Tr
where "r" is a subscript used to indicate that values for the return tripe.
We are given the time for each trip: 6 hours and then 8 hours for the return trip.
D = R * 6
Dr = Rr * 8
And the rate for both trips is based on x -- the speed in still air. It is x + 22 in one direction and x - 22 in the other.
D = (x + 22) * 6
Dr = (x - 22) * 8
Finally, we know that the distance is the same for both trips.
D = Dr
Therefore, through transitibity, we know that the right sides of both of equations are equal.
(x + 22) * 6 = (x - 22) * 8
6(x + 22) = 8(x - 22)
Solve that and you will get 154.
Answer this Question
More Related Questions
- math - An airplane flew for 6 hours with a 22km/hour tailwind. The return flight...
- Algebra - Beth is a bush pilot in Alaska. On a recent trip, she flew 600 miles ...
- repost math question - An aircraft flew 6 hours with the wind. The return trip ...
- algebra II - An aircraft flew 6 hours with the wind. The return trip took 7 ...
- math - The average airspeed of a single-engine aircraft is 150 milesper hour. If...
- math - In a storm, a plane flew against the wind and took 9 hours to cover 3,...
- 8th Algebra - 1) An airplane took 2 hours to fly 600 km against a head wind. The...
- algebra - An airplane encountered a head wind during a flight between Rontown ...
- Algebra: 8th Grade; Equation Check - 1) A private airplane leaves an airport and...
- Math - An airplane flying into a headwind travels the 2800 mile flying distance ...