SOLUTION: A river is one kilometer wide and flows with a uniform stream velocity. A ship sailing at full speed needs 12 minutes to cover one kilometer upstream, and 3 minutes to cover one ki
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Question 830766: A river is one kilometer wide and flows with a uniform stream velocity. A ship sailing at full speed needs 12 minutes to cover one kilometer upstream, and 3 minutes to cover one kilometer downstream. What is the shortest time in which the ship can cross the river to the nearest point on the opposite bank?
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
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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)
---
put the system of linear equations into standard form:
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12(x - y) = 1
3(x + y) = 1
---
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:
https://sooeet.com/math/system-of-linear-equations-solver.php
---
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
---
s = d/t
t = d/s
---
t = (1 km) / (0.16666666 km/min)
t = 6.0 min
---
answer:
time required to cross the 1-kilometer wide river to the nearest point on the opposite bank = 6 minutes
---
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:
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