SOLUTION: Alvin paddled 8 miles upstream in 2 hours. He paddled 16 miles downstream in the same time. Find the speed that Alvin paddled in still water and the speed of the current

Question 829340: Alvin paddled 8 miles upstream in 2 hours. He paddled 16 miles downstream in the same time. Find the speed that Alvin paddled in still water and the speed of the current
Found 2 solutions by TimothyLamb, josmiceli:
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
---
x = boat speed
y = current speed
---
s = d/t
---
x - y = 8/2
x + y = 16/2
---
put the system of linear equations into standard form:
---
x - y = 4
x + y = 8
---
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 = boat speed = 6 mph
y = current speed = 2 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 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = his speed paddling in still water
Let = the speed of the current
----------------
Paddling upstream:
(1)
Paddling downstream:
(2)
---------------------
(1)
(2)
Add the equations

and
(1)
(1)
(1)
(1)
Alvin paddled 6 mi/hr in still water
and the speed of the current is 2 mi/hr
----------------------------------
check:
(2)
(2)
and
(1)
(1)
OK

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