<PRE><B>Question 830766</B>
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x = ship speed
y = water speed
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s = d/t
t = d/s
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up:
12 = 1/(x - y)
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down:
3 = 1/(x + y)
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linear system:
12 = 1/(x - y)
3 = 1/(x + y)
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put the system of linear equations into standard form:
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12(x - y) = 1
3(x + y) = 1
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12x - 12y = 1
3x + 3y = 1
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copy and paste the above linear system in standard form into this matrix-method solver:
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speeds:
x = ship speed = 0.20833333 km/min
y = water speed = 0.125 km/min
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perpendicular river crossing, 1-km bank to bank:
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make a right triangle with:
hypotenuse = ship speed 
side-a = water speed
side-b = net ship speed
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hh = aa + bb
bb = hh - aa
b = sqrt( hh - aa )
b = sqrt( 0.20833333^2 - 0.125^2 )
b = 0.16666666 km/min
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s = d/t
t = d/s
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t = (1 km) / (0.16666666 km/min)
t = 6.0 min
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answer:
time required to cross the 1-kilometer wide river to the nearest point on the opposite bank = 6 minutes
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Solve and graph linear equations:
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Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
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Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php</PRE>