Question 141992: ii. You participate in a triathlon in which you swam 3 miles, ran 5 miles, and then bicycled 10 miles. You ran twice as fast as you swam, and cycled three times as fast as you swam. If your total time was 1 hr and 46 minutes, how fast did you swim?
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website!
Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let r=swimming rate
Then 2r=running rate
And 3r=cycling rate
Amount of time that you swam=3/r
Amount of time that you ran=5/2r
Amount of time that you cycled=10/3r
Now we are told that the above times add up 1hr 46 min or 106 min (Note: we can't deal in both hours and minutes. We have to deal in one or the other so let's deal in minutes. By doing this, our answer will come out in miles/minute and we'll have to change it to miles/hr which is easy- we just multiply by 60--ok?)
So:
3/r+ 5/2r + 10/3r=106 multiply each term by 6r
18+15+20=636r collect like terms
53=636r divide both sides by 636
r=0.0833333333333333-- miles/min
Multiply this by 60 and we have swimming rate in miles/hr, so
r=60*(0.083333333333333333333--)=5 miles/hr
CK
3/5+5/10+10/15=1 46/60=106/60=53/30
(18+15+20)/30=53/30
53/30=53/30
Hope this helps---ptaylor
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