SOLUTION: with a head wind, a plane traveled 1000 miles in 4 hours. with the same wind as a tail wind, the return trip took 3 hours 20 minutes. find the wind speed.

Question 825589: with a head wind, a plane traveled 1000 miles in 4 hours. with the same wind as a tail wind, the return trip took 3 hours 20 minutes. find the wind speed.
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
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x = airplane speed
y = wind speed
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s = d/t
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head:
x - y = 1000/4
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tail:
x + y = 1000/(3+(20/60))
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system:
x - y = 1000/4
x + y = 1000/(3+(20/60))
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put the system of linear equations into standard form
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x - y = 250
x + y = 300
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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 = 275 mph
y = wind speed = 25 mph
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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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Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Solve systems of linear equations up to 4-equations 4-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
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