CEMC Fermat, 2025

Algebra Difficulty 2.6 Junior Find the answer Canada

In a $\text{2000 m}$ race,
Arturo, Morgan and Henri run at constant but different speeds. Arturo
finishes $\text{200 m}$ ahead of
Morgan and $\text{290 m}$ ahead of
Henri. If Morgan and Henri each continue at their same speeds, how far
ahead of Henri will Morgan finish?

Pick one

Solution

When Arturo finishes the race, he is $200 \text{ m}$ ahead of Morgan and $290 \text{ m}$ ahead of Henri.

This means that Morgan runs $2000 \text{ m} - 200 \text{ m}=1800 \text{ m}$ in the same amount of time that it
takes Henri to run $2000 \text{ m} - 290 \text{ m}=1710 \text{ m}$ .

If they each continue at their same speeds, Morgan runs the last $\dfrac{1800 \text{ m}}{9}=200 \text{ m}$
of the race in the same amount of time that Henri runs $\dfrac{1710 \text{ m}}{9}=190 \text{ m}$ .

Therefore, Morgan completes the $1800 \text{ m} + 200 \text{ m}=2000 \text{ m}$ race in the same amount of
time that Henri runs $1710 \text{ m} + 190 \text{ m}=1900 \text{ m}$ . Morgan finishes the race 100 m ahead
of Henri.

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