# math

during a triathlon, Sharon swims 1/4 of the total route and cycles 3/5 of the remaining route. she runs the rest of the route. if she runs 3,600 meters, find the total distance of the triathlon route. show your work.

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1. done, look below to your last post of this

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posted by Reiny
2. Sharon swims 1/4 of the total route
Swim = (1/4)*TotRoute
Sharon cycles 3/5 of the remaining route
Cycles = (3/5)*(3/4)*TotRoute
Notice the 3/4. If she swam 1/4 of the total route, 3/4 of the route remains for cycling and running.
Sharon runs rest of the route
Runs = (2/5)*(3/4)*TotRoute = 3,600 meters
2/5 of the remaining route is what is left after the 3/5 of the remaining route of cycling

Solve the Runs equation first
3,600 meters = (6/20)*TotRoute
Solve for TotRoute
The answer is TotRoute = 12,000 meters

You can also solve for swim and cycle if you wish. Plug back into the other equations

Swim = (1/4)*TotRoute = (1/4)*12,000 meters = 3,000 meters

Cycles = (3/5)*(3/4)*TotRoute = (3/5)*(3/4)*12,000 meters = 5,400 meters

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posted by Jeff

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