# Problem of the Week Problem A and Solution Tri Kids Race

## Problem

A triathlon is a race that has three components. Racers first complete a swimming component, then they complete a biking component, and finally they complete a running component.

In the Tri Kids race, the racers first swim $$100$$ m. They then travel $$25$$ m to the bicycle area. The racers then ride their bike in a $$3$$ km long loop back to the bicycle area. The bicycle area is right beside the track. The racers then run $$3$$ laps of the track to finish the race. One lap of the track is $$400$$ m.

In the Tri Kids race, what is the total distance the racers have to cover, from start to finish?

## Solution

To calculate the total distance, we can convert all measurements to metres. The distance travelled on their bike is $$3$$ km. Since $$1$$ km is equal to $$1000$$ m, then $$3$$ km is equal to $$3 \times 1000 = 3000$$ m.

To calculate the distance the racers have to run, we multiply $$3 \times 400 = 1200$$ m.

We can add up the distances travelled in the swim, transition to the bicycle area, bike, and run. The total distance covered is: $$100 + 25 + 3000 + 1200 = 4325$$ m.

Alternatively, we can enumerate the distances travelled in a table:

Race Component Distance of Component Total Distance Travelled
Swim $$100$$ m $$100$$ m
Transition $$25$$ m $$125$$ m
Bike $$3$$ km $$= 3000$$ m $$3125$$ m
Lap $$1$$ $$400$$ m $$3525$$ m
Lap $$2$$ $$400$$ m $$3925$$ m
Lap $$3$$ $$400$$ m $$4325$$ m