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
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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
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s = d/t
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x - y = 8/2
x + y = 16/2
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put the system of linear equations into standard form:
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x - y = 4
x + y = 8
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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 = boat speed = 6 mph
y = current speed = 2 mph
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system matrix
1 -1
1 1
---
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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---
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---
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You can put this solution on YOUR website! Let = his speed paddling in still water
Let = the speed of the current
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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
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check:
(2)
(2)
and
(1)
(1)
OK
