Question 403213
Let {{{k}}} = rate of swimming without current
Let {{{c}}} = rate of current
{{{k - c}}} = rate of swimming against current
{{{k + c}}} = rate of swimming with current
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given:
(1) {{{200 = (k - c)*8}}} meters
(2) {{{200 = (k + c)*4}}} meters
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This is 2 equations and 2 unknowns, so it's solvable
(1) {{{8k - 8c = 200}}}
(2) {{{4k + 4c = 200}}}
Multiply both sides of (2) by {{{2}}}
and add the equations
(1) {{{8k - 8c = 200}}}
(2) {{{8k + 8c = 400}}}
{{{16k = 600}}}
{{{k = 37.5}}}
and, from (2),
(2) {{{k + c = 50}}}
{{{ c = 12.5}}}
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Always use the definition (ave. speed) = (total distance)/(total time)
His ave. speed = {{{(200 + 200)/(8 + 4) = 400/12}}}
{{{400/12 = 33.333}}} m/min
The speed of the current is 12.5 m/min