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) About Me  (Show Source):
You can put this solution on YOUR website!
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x = boat speed
y = current speed
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s = d/t
---
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
---
determinant of system matrix = 2
---
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---
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---
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Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = his speed paddling in still water
Let +c+ = the speed of the current
----------------
Paddling upstream:
(1) +8+=+%28+s+-+c+%29%2A2+
Paddling downstream:
(2) +16+=+%28+s%2Bc+%29%2A2+
---------------------
(1) +2s+-+2c+=+8+
(2) +2s+%2B+2c+=+16+
Add the equations
+4s+=+24+
+s+=+6+
and
(1) +2s+-+2c+=+8+
(1) +s+-+c+=+4+
(1) +6+-+c+=+4+
(1) +c+=+2+
Alvin paddled 6 mi/hr in still water
and the speed of the current is 2 mi/hr
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check:
(2) +16+=+%28+6%2B2+%29%2A2+
(2) +16+=+16+
and
(1) +8+=+%28+6+-+2+%29%2A2+
(1) +8+=+8+
OK