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.
x(1 - 1/4 - (3/4)(3/5)) = 3600
To find the total distance of the triathlon route, we need to add the distances of the swimming, cycling, and running portions together.
Let's start by finding the distance Sharon swims, which is 1/4 of the total route. Since we're given that she runs 3,600 meters, we can use this information to find the distance of the swimming portion.
We know that the running portion is the rest of the route after swimming and cycling, so:
Running distance = Total distance - Swimming distance - Cycling distance
Since Sharon runs 3,600 meters and the running portion is the rest of the route, we have:
3,600 = Total distance - Swimming distance - Cycling distance
Now let's find the distance Sharon cycles. We're told that she cycles 3/5 of the remaining route after swimming. So the distance Sharon cycles is:
Cycling distance = (3/5) * Remaining distance after swimming
Since we already know the distance Sharon runs (3,600 meters) and the equation for the running portion, we can substitute these values into the equation to get:
3,600 = Total distance - Swimming distance - (3/5) * Remaining distance after swimming
Now let's substitute the swimming distance with the fraction of the total route:
Swimming distance = (1/4) * Total distance
Plugging this into the equation:
3,600 = Total distance - (1/4) * Total distance - (3/5) * Remaining distance after swimming
Simplifying the equation:
3,600 = Total distance - (1/4) * Total distance - (3/5)(Total distance - Swimming distance)
Now we can solve for the remaining distance after swimming:
Remaining distance after swimming = Total distance - Swimming distance
Substituting this back into the equation:
3,600 = Total distance - (1/4) * Total distance - (3/5)(Total distance - (1/4) * Total distance)
Simplifying further:
3,600 = Total distance - (1/4) * Total distance - (3/5)(Total distance - (1/4) * Total distance)
Now we can solve for the Total distance:
Total distance = 3,600 / (1 - 1/4 - 3/5)
Simplifying the expression further:
Total distance = 3,600 / (4/4 - 1/4 - 12/20)
Total distance = 3,600 / (16/20 - 4/20 - 12/20)
Total distance = 3,600 / (16/20 - 16/20)
Total distance = 3,600 / 0
Since division by zero is undefined, we cannot divide 3,600 by 0. Therefore, there might be a mistake in the given information or calculations.
Please double-check the values and calculations provided to rectify this situation.