During a triathlon, tansneem swims 1 over 4 of the total route and cycles 3 over 5 of the remaining route. She runs the rest of the route. If she runs 3600 m, determine the total distance of the triathlon
Let the total distance of the triathlon be D.
Tansneem swims 1/4D of the total distance, so she swims (1/4)D.
The remaining distance after swimming is D - (1/4)D = (3/4)D.
Tansneem cycles 3/5 of the remaining distance, so she cycles (3/5)(3/4)D = (9/20)D.
The distance that Tansneem has left to run is (3/4)D - (9/20)D = (15/20)D - (9/20)D = (6/20)D = (3/10)D.
Since she runs 3600 m, we can set up the equation (3/10)D = 3600.
Multiplying both sides by 10/3, we get D = 3600 * 10/3.
Dividing 3600 by 3 and multiplying by 10, we get D = 36000/3 = 12000.
Therefore, the total distance of the triathlon is D = 12000 meters.
Let's break down the problem step-by-step:
Step 1: Find the distance Tanseem cycles.
- Tanseem swims 1/4 of the total route, so 3/4 of the total route remains.
- Out of this remaining route, Tanseem cycles 3/5 of the distance.
- Let's represent the total distance of the triathlon as "D".
- Therefore, the distance Tanseem cycles is (3/5) * (3/4) * D.
Step 2: Find the distance Tanseem swims.
- Tanseem swims 1/4 of the total route.
- Therefore, the distance Tanseem swims is (1/4) * D.
Step 3: Find the distance Tanseem runs.
- Tanseem runs the rest of the route after swimming and cycling.
- The distance Tanseem runs is equal to the total distance minus the distances she swims and cycles.
- Therefore, the distance Tanseem runs is D - [(3/5) * (3/4) * D] - [(1/4) * D].
Step 4: Set up the equation.
- We know that the distance Tanseem runs is 3600 m.
- Therefore, we can solve the equation:
D - [(3/5) * (3/4) * D] - [(1/4) * D] = 3600.
Step 5: Solve the equation.
- Combining like terms, the equation becomes:
D - (9/20) * D - (1/4) * D = 3600.
(20/20) * D - (9/20) * D - (1/4) * D = 3600.
(20 - 9 - 5)/20 * D = 3600.
6/20 * D = 3600.
- Simplifying, the equation becomes:
(3/10) * D = 3600.
- Multiplying both sides by 10/3, we get:
D = 3600 * (10/3).
D = 12,000 m.
Therefore, the total distance of the triathlon is 12,000 meters.
To determine the total distance of the triathlon, we need to find the distances for each segment of the race.
Let's assume the total distance of the triathlon is "x" meters.
Tansneem swims 1 over 4 of the total route, which means she swims (1/4) * x distance.
The remaining distance after swimming would be (3/4) * x.
Tansneem cycles 3 over 5 of the remaining route, which means she cycles (3/5) * (3/4) * x distance.
The distance remaining after cycling is (2/5) * (3/4) * x.
Finally, we know that Tansneem runs 3600 meters, which is equal to the distance remaining after cycling.
So, we can set up the equation:
(2/5) * (3/4) * x = 3600
To solve for x, we can simplify the equation:
(2/5) * (3/4) * x = 3600
(6/20) * x = 3600
(3/10) * x = 3600
Now we can solve for x by multiplying both sides of the equation by (10/3):
x = (3600 * 10) / 3
x = 12,000
Therefore, the total distance of the triathlon is 12,000 meters.