SOLUTION: Joe can run twice as fast as Pete. They start at the same point and run opposite directions for 40 minutes. The distance between them now is 16 km. How fast does Joe run.

Question 825229: Joe can run twice as fast as Pete. They start at the same point and run opposite directions for 40 minutes. The distance between them now is 16 km. How fast does Joe run.
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
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x = joe speed
y = pete speed
---
x = 2y
---
relative speed:
s = x + 2y
---
s = d / t
s = 16/(40/60)
s = (3*16)/2
---
s = 24 kph
s = x + 2y
x + 2y = 24
---
linear system:
x = 2y
x + 2y = 24
---
put the system of linear equations into standard form
---
x - 2y = 0
x + 2y = 24
---
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 = joe speed = 12 kph
y = pete speed = 6 kph
---
system matrix
1 -2
1 2
---
inverse of system matrix
0.5 0.5
-0.25 0.25
---
determinant of system matrix = 4
---
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 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
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