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Algebra Difficulty 2.6 Junior Find the answer Canada

In a 2000 m\text{2000 m} race,
Arturo, Morgan and Henri run at constant but different speeds. Arturo
finishes 200 m\text{200 m} ahead of
Morgan and 290 m\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 m200 \text{ m} ahead of Morgan and 290 m290 \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 1800 m9=200 m\dfrac{1800 \text{ m}}{9}=200 \text{ m}
of the race in the same amount of time that Henri runs 1710\text{1710} 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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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.