Question 786489
Mar T. Ello participated in a triathlon in which he swam 3 miles, ran 5 miles and then bicycled 10 miles. Mar ran twice as fast as he swam, and he cycled three times as fast as he swam. If his total time for the triathlon was 1 hour and 46 minutes, then how fast did he swim?
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Let 

His swimming speed = x miles/hour
</pre>
Mar ran twice as fast as he swam,
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So

His running speed = 2x miles/hour
</pre>
he cycled three times as fast as he swam
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So 

His bicycling speed = 3x miles hour.
</pre>
he swam 3 miles
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Since TIME = {{{DISTANCE/SPEED}}} he swam for {{{3/x}}} of an hour
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ran 5 miles 
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Since TIME = {{{DISTANCE/SPEED}}} he swam for {{{5/(2x)}}} of an hour
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and then bicycled 10 miles
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Since TIME = {{{DISTANCE/SPEED}}} he swam for {{{10/(3x)}}} of an hour

Total time = {{{3/x}}}{{{""+""}}}{{{5/(2x)}}}{{{""+""}}}{{{10/(3x)}}}
</pre>
his total time for the triathlon was 1 hour and 46 minutes
<pre>
So we set the expression for the total time equal to {{{1&46/60}}}{{{""=""}}}{{{1&23/30}}}{{{""=""}}}{{{53/30}}} hours

{{{3/x}}}{{{""+""}}}{{{5/(2x)}}}{{{""+""}}}{{{10/(3x)}}} {{{""=""}}} {{{53/30}}}

Clear of fractions by multiplying through by the LCD of 30x

90 + 75 + 100 = 53x
          265 = 53x
          {{{265/53}}} = x
            5 = x

His swimming speed = x miles/hour = 5 miles/hour
His running speed = 2x miles/hour = 2(5) = 10 miles/hour
His bicycling speed = 3x miles hour = 3(5) = 15 miles/hour.

Edwin</pre>