SOLUTION: A plane can fly 1315km in 70 minutes with the wind. Flying against the wind,the plane travels the same distance in 65minutes. Find the speed of the wind and the speed of the plane
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Question 825259: A plane can fly 1315km in 70 minutes with the wind. Flying against the wind,the plane travels the same distance in 65minutes. Find the speed of the wind and the speed of the plane in still air.
You can put this solution on YOUR website! ---
x = airplane speed
y = wind speed
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s = d / t
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x + y = 1315/(70/60)
x - y = 1315/(65/60)
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put the system of linear equations into standard form
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x + y = 1127.142857142857110
x - y = 1213.846153846154039
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copy and paste the above linear system in standard form into this matrix-method solver:
https://sooeet.com/math/system-of-linear-equations-solver.php
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solution:
x = airplane speed = 1170.4945 kph
y = wind speed = -43.351648 kph
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NOTE:
the negative wind speed indicates that there is an error in the problem statement.
the error is obvious: an airplane cannot fly a fixed distance AGAINST the wind in LESS time than it takes to fly the same distance WITH the wind, assuming that the airplane's airspeed is the same during both the upwind and downwind segments of the flight.
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system matrix
1 1
1 -1
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inverse of system matrix
0.5 0.5
0.5 -0.5
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determinant of system matrix = -2
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