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At the local triathlon, competitors travel a total distance of 20 km. They cycle [tex]\frac{4}{5}[/tex] of the distance, run [tex]\frac{3}{4}[/tex] of the distance, and swim [tex]\frac{1}{4}[/tex] of the distance.

a. How far do the competitors cycle?
[tex]\frac{4}{5} \times \frac{20}{1} = \frac{80}{5} = 16 \text{ km}[/tex]

b. How far do the competitors run?
[tex]\frac{3}{4} \times 20 = \frac{60}{4} = 15 \text{ km}[/tex]

c. How far do the competitors swim?
[tex]\frac{1}{4} \times 20 = \frac{20}{4} = 5 \text{ km}[/tex]

Answer :

Sure! Let's break down each part of the question and calculate the distances involved in the triathlon for cycling, running, and swimming.

a. How far do the competitors cycle?

The competitors cycle [tex]\(\frac{4}{5}\)[/tex] of the total distance. To find out how far they cycle, you multiply the fraction by the total distance:

[tex]\[
\frac{4}{5} \times 20 = 16 \text{ km}
\][/tex]

So, competitors cycle 16 km.

b. How far do the competitors run?

The competitors run [tex]\(\frac{3}{4}\)[/tex] of the total distance. To calculate this, multiply the fraction by the total distance:

[tex]\[
\frac{3}{4} \times 20 = 15 \text{ km}
\][/tex]

Thus, the competitors run 15 km.

c. How far do the competitors swim?

The competitors swim [tex]\(\frac{1}{4}\)[/tex] of the total distance. To find out the swimming distance, you multiply the fraction by the total distance:

[tex]\[
\frac{1}{4} \times 20 = 5 \text{ km}
\][/tex]

So, the competitors swim 5 km.

In summary:
- Cycling distance: 16 km
- Running distance: 15 km
- Swimming distance: 5 km

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