In a race, a triathlete runs 1/3 of total distance, cycles 2/5 of the total diatance and swims the ramaining distance. he swim 1.200 meters. What is the

total distance of the race?

Let's make it all the same denominators.

1/3 = 5/15. 2/5 = 6/15

5/15 + 6 /15 = 11/15

15/15 - 11/15 = 4/15

4/15 is the total fraction he swims.

If 1200 is 4/15 then we divide 1200 by 4 which is 300.

1/15 is 300.

300× 15 = 4500

4500 meters is the total distance if the race.

Ouch! I got confused on the period/comma usage disparity.

Or, I could just say I was figuring in km instead of meters!

To find the total distance of the race, we need to determine the distance covered in the running and cycling segments. Let's calculate that step by step.

Let's assume the total distance of the race is "d" meters.

The triathlete runs 1/3 of the total distance, which can be expressed as (1/3) * d = (d/3) meters.

The triathlete cycles 2/5 of the total distance, which can be expressed as (2/5) * d = (2d/5) meters.

Finally, the remaining distance is covered by swimming, which is given as 1,200 meters.

Now, we can set up an equation to solve for the total distance "d" by adding the distances covered in each segment:

(d/3) + (2d/5) + 1,200 = d

To simplify the equation, let's clear the fractions by multiplying everything by 15 (the least common multiple of 3 and 5):

5d + 6d + 18,000 = 15d

11d + 18,000 = 15d

Rearranging the equation, we have:

15d - 11d = 18,000

4d = 18,000

Dividing both sides by 4:

d = 18,000 / 4

d = 4,500

Therefore, the total distance of the race is 4,500 meters.

Let x = total distance

x - 1/3x - 2/5x = 1,200m

Solve for x.

x(1 - 1/3 - 2/5) = 6/5

4/15 x = 6/5
x = 9/2

check:
1/3 of 9/2 = 3/2 = 1.5
2/5 of 9/2 = 9/5 = 1.8
1.5 + 1.8 + 1.2 = 4.5 = 9/2