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 if the route
total distance ---- x m
(1/4)x + (3/5)(3/4)x + 3600 = x
multiply each term by 20 , the LCD
5x + 9x + 72000 = 20x
6x = 72000
x = 12000 m
looks like she did a 12 K triathlon
Let's assume the total distance of the route is represented by "x" meters.
According to the given information, Sharon swims 1/4 of the total route. Therefore, the distance she swims is (1/4) * x.
After swimming, Sharon has (3/4) * x distance remaining. She then cycles 3/5 of this remaining distance. Hence, the cycling distance is (3/5) * (3/4) * x.
After swimming and cycling, Sharon is left with (2/5) * (3/4) * x distance to run, which is equal to 3,600 meters.
We can set up the equation:
(2/5) * (3/4) * x = 3,600
Now, let's solve for x.
Multiply both sides by (5/2) * (4/3):
x = (3,600) * (5/2) * (4/3)
Simplifying this expression:
x = 12,000 meters
Therefore, the total distance of the route is 12,000 meters.
To find the total distance of the route, let's work through the given information step by step.
1. Sharon swims 1/4 of the total route.
Let's assume the total route distance is 'x' meters.
So, Sharon swims (1/4) * x meters.
2. After swimming, Sharon cycles 3/5 of the remaining route.
The remaining route distance after swimming would be (x - (1/4)x) meters.
So, Sharon cycles (3/5) * (x - (1/4)x) meters.
3. Finally, Sharon runs the rest of the route, which is 3,600 meters.
The remaining route distance after swimming and cycling would be (x - (1/4)x) - (3/5) * (x - (1/4)x) meters.
Simplifying this expression, (x - (1/4)x) - (3/5) * (x - (1/4)x) = 3600 meters.
Now, we can solve the equation to find the value of 'x', which is the total distance of the route.
Let's calculate this:
(x - (1/4)x) - (3/5) * (x - (1/4)x) = 3600
Simplify the equation:
(x - (1/4)x) - (3/5) * (x - (1/4)x) = 3600
x - (1/4)x - (3/5) * x + (3/20)x = 3600
x - (1/4)x - (3/5)x + (3/20)x = 3600
[(20x - 5x - 12x + 3x)/20] = 3600
(6x/20) = 3600
Simplify further:
6x = 3600 * 20
6x = 72000
x = 72000 / 6
x = 12000
Therefore, the total distance of the route is 12,000 meters.