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?
Let
His swimming speed = x miles/hour
Mar ran twice as fast as he swam,
So
His running speed = 2x miles/hour
he cycled three times as fast as he swam
So
His bicycling speed = 3x miles hour.
he swam 3 miles
Since TIME = 
he swam for 
of an hour
ran 5 miles
Since TIME = he swam for 
of an hour
and then bicycled 10 miles
Since TIME = he swam for 
of an hour
Total time = 
his total time for the triathlon was 1 hour and 46 minutes
So we set the expression for the total time equal to 
hours
Clear of fractions by multiplying through by the LCD of 30x
90 + 75 + 100 = 53x
265 = 53x
= 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
