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.
Algebra ->
Customizable Word Problem Solvers
-> Travel
-> 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.
Log On
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! ---
x = airplane speed
y = wind speed
---
s = d/t
---
head:
x - y = 1000/4
---
tail:
x + y = 1000/(3+(20/60))
---
system:
x - y = 1000/4
x + y = 1000/(3+(20/60))
---
put the system of linear equations into standard form
---
x - y = 250
x + y = 300
---
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
---
solution:
x = airplane speed = 275 mph
y = wind speed = 25 mph
---
system matrix
1 -1
1 1
---
inverse of system matrix
0.5 0.5
-0.5 0.5
---
determinant of system matrix = 2
---
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
