During a triathlon, Susan swims 1/4 of the total route and cycles 3/5 of the renaming route. She runs the rest of the route. If she runs 3,600 meters, find the total distance of the triathlon route?
R=3600
D=1/2 D+ 3/5 D + 3600
D(10-5-3)/10=3600
D=5*3600
check that.
To find the total distance of the triathlon route, we need to add up the distances Susan swims, cycles, and runs.
Let's assign variables:
Let "x" represent the total distance of the triathlon.
Susan swims 1/4 of the total distance, which is (1/4)*x.
Susan cycles 3/5 of the remaining distance after swimming, which is (3/5)*(3/4)x.
Susan runs 3600 meters.
The total distance of the triathlon route is the sum of these three distances:
x = (1/4)*x + (3/5)*(3/4)x + 3600.
Let's solve the equation to find the value of x:
First, let's simplify the equation:
x = (1/4)x + (9/20)x + 3600.
To solve the equation, we'll combine like terms:
x = (1/4 + 9/20)x + 3600.
Finding a common denominator for (1/4 + 9/20):
x = (5/20 + 9/20)x + 3600.
Combine the fractions:
x = (14/20)x + 3600.
To get rid of the fraction, multiply both sides of the equation by 20:
20x = 14x + 72000.
Subtract 14x from both sides:
6x = 72000.
Divide both sides by 6:
x = 72000/6.
Simplifying the expression:
x = 12000.
Therefore, the total distance of the triathlon route is 12000 meters.