Question 387782
Rate*Time=Distance
{{{R*t=D}}}
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Let the current speed be C.
With the current,
{{{(15+C)*t=80}}}
{{{t=80/(15+C)}}}
Against the current,
{{{(15-C)*(t+4)=80}}}
{{{t+4=80/(15-C)}}}
Subsituting,
{{{80/(15+C)+4=80/(15-C)}}}
Use the common denominator, {{{(15-C)(15+C)}}}
{{{(80(15+C))/((15-C)(15+C))+(4(15-C)(15+C))/((15-C)(15+C))=(80(15+C))/((15-C)(15+C))}}}
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{{{(80(15-C)+4(15-C)(15+C)-80(15+C))/((15-C)(15+C))=0}}}
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{{{(1200-80C+900-4C^2-1200-80C)/((15-C)(15+C))=0}}}
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{{{(900-160C-4C^2)/((15-C)(15+C))=0}}}
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{{{(225-40C-C^2)/((15-C)(15+C))=0}}}
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{{{((5-C)(45+C))/((15-C)(15+C))=0}}}
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Only one solution since {{{C>=0}}}
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{{{highlight(C=5)}}}mph