SOLUTION: 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 swa

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

RELATED QUESTIONS
You participate in a triathlon in which you swam three miles, ran five miles and then... (answered by orca)

Mar T. Ello participated in a triathlon in which he swam 3 miles, ran 5 miles and then... (answered by Edwin McCravy)

I have a word problem that I cannot get into the right form. If I can get it into the... (answered by rwm)

In a special triathlon, Betty swam 2 miles in 25 minutes, biked 30 miles in 45... (answered by checkley79)

Salazar only ran 50 miles in one week. While Rodgers ran twice as many miles as Salazar.... (answered by stanbon)

if you ran 100 yards in 9.8 seconds how fast were you going in miles per... (answered by ankor@dixie-net.com)

Eric is preparing to run in the Bay Marathon. One day, he ran and walked a total of 16... (answered by checkley75)

If you ran 3 miles in one hour how long did it take you to run one and three fourths of a (answered by ewatrrr)

In a charity triathlon, Mark ran half the distance and swam a quarter of the distance.... (answered by JulietG)