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.
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
done, look below to your last post of this
Thx that helps me so much
Ah, triathlons! A great way to test one's endurance and enjoy some quirky exercise. Let's dive into the math!
We know that Sharon runs 3,600 meters, which is the remaining distance after swimming and cycling. So, let's set up an equation to solve for the total distance of the triathlon route.
Let's represent the total distance as "x".
Sharon swims 1/4 of the total distance: (1/4)x
The remaining distance after swimming is 3/4 of the total distance.
Sharon cycles 3/5 of the remaining distance: (3/5)(3/4)x = (9/20)x
We now know that Sharon runs the rest of the distance: 3,600 meters.
So, we can set up our equation:
(9/20)x = 3,600
To solve for "x," we'll multiply both sides by the reciprocal of (9/20):
x = 3,600 * (20/9)
x = 8,000 meters
Ta-da! The total distance of the triathlon route is 8,000 meters. Sharon has quite the adventure ahead of her! Keep those legs pumping, Sharon!
To find the total distance of the triathlon route, we can work backwards step by step.
First, let's find the distance Sharon cycled. It is given that she swims 1/4 of the total route, so she cycles the remaining 3/4 of the route. Since she runs the last portion, the distance she cycles is equal to 3/5 of the remaining 3/4 of the total route.
To calculate the distance Sharon cycled, we can follow these steps:
1. Calculate the remaining distance after swimming:
Total distance - Distance swam = Remaining distance
Let's denote the total distance as "D" and the distance swam as "D/4":
D - D/4 = 3D/4
2. Calculate the distance Sharon cycled:
Distance cycled = (3/5) * (3D/4)
Simplifying, we get:
Distance cycled = (9D/20)
Next, let's find the distance Sharon ran. It is given that she ran 3,600 meters, which is the remaining portion after swimming and cycling.
To calculate the total distance, we can add up the distances swam, cycled, and ran:
Total distance = Distance swam + Distance cycled + Distance ran
Since we already know the distance she ran and the distance swam (D/4), we can substitute those values:
Total distance = D/4 + 9D/20 + 3600
To find the value of D, we can solve this equation. We'll follow these steps:
1. Combine like terms:
Total distance = (1/4)D + (9/20)D + 3600
2. Find a common denominator:
Total distance = (5/20)D + (9/20)D + 3600
3. Add the numerators:
Total distance = (14/20)D + 3600
4. Simplify the fractions:
Total distance = (7/10)D + 3600
To isolate D, we subtract 3600 from both sides:
Total distance - 3600 = (7/10)D
Finally, we divide both sides by (7/10) to solve for D:
[(Total distance - 3600) / (7/10)] = D
Thus, the total distance of the triathlon route is given by [(Total distance - 3600) / (7/10)].