Question 994638
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r=rate of river
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Upstream:
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{{{time[upstream]=distance/rate}}}
{{{time[upstream]=(5km)/(20kph-r)}}}
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Downstream:
{{{time[downstream]=distance/rate}}}
{{{time[downstream]=10km/(20kph+r)}}}
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Since {{{time[upstream]=time[downstream]}}}:
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{{{5km/(20kph-r)=10km/(20kph+r)}}}
{{{(5km)(20kph+r)=(10km)(20kph-r)}}}
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{{{(100km^2)_per_hr+5r_km=(200km^2)_per_hr-10r_km}}}
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{{{15r_km=(100km^2)_per_hr}}}
r=6.667 km/hr
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ANSWER: The speed of the current was 6.667 kilometers per hour.
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CHECK:
{{{time[upstream]=time[downstream]}}}
{{{5km/(20kph-6.667kph)=10km/(20kph+6.667kph)}}}
{{{5km/13.333kph=10km/20.667kph}}}
{{{0.375hr=0.375hr}}}