Greg, Charlize, and Azarah run at different but constant speeds. Each pair ran a race on a track that measured $100 \mathrm{~m}$ from start to finish. In the first race, when Azarah crossed the finish line, Charlize was $20 \mathrm{~m}$ behind. In the second race, when Charlize crossed the finish line, Greg was $10 \mathrm{~m}$ behind. In the third race, when Azarah crossed the finish line, how many metres was Greg behind?
(A) 20
(B) 25
(C) 28
(D) 32
(E) 40
Solution 1

In the first race, when Azarah crossed the finish line, Charlize was $20 \mathrm{~m}$ behind or Charlize had run $80 \mathrm{~m}$.

Since Azarah and Charlize each travelled these respective distances in the same amount of time, then the ratio of their speeds is equal to the ratio of their distances travelled, or $100: 80$.

Similarly in the second race, when Charlize crossed the finish line, Greg was $10 \mathrm{~m}$ behind or Greg had run $90 \mathrm{~m}$.

Since Charlize and Greg each travelled these respective distances in the same amount of time, then the ratio of their speeds is equal to the ratio of their distances travelled, or $100: 90$.

Let $A, C$ and $G$ represent Azarah's, Charlize's and Greg's speeds, respectively.

Then, $A: C=100: 80=25: 20$ and $C: G=100: 90=20: 18$.

Therefore, $A: C: G=25: 20: 18$ and $A: G=25: 18=100: 72$.

Over equal times, the ratio of their speeds is equal to the ratio of their distances travelled.

Therefore, when Azarah travels $100 \mathrm{~m}$, Greg travels $72 \mathrm{~m}$.

When Azarah crossed the finish line, Greg was $100-72=28 \mathrm{~m}$ behind.

## Solution 2

In the first race, when Azarah crossed the finish line, Charlize was $20 \mathrm{~m}$ behind or Charlize had run $80 \mathrm{~m}$.

Since Azarah and Charlize each travelled these respective distances in the same amount of time, then the ratio of their speeds is equal to the ratio of their distances travelled, or $100: 80$.

That is, Charlize's speed is $80 \%$ of Azarah's speed.

Similarly, Greg's speed is $90 \%$ of Charlize's speed.

Therefore, Greg's speed is $90 \%$ of Charlize's speed which is $80 \%$ of Azarah's speed, or Greg's speed is $90 \%$ of $80 \%$ of Azarah's speed.

Since $90 \%$ of $80 \%$ is equivalent to $0.90 \times 0.80=0.72$ or $72 \%$, then Greg's speed is $72 \%$ of Azarah's speed.

When Azarah ran $100 \mathrm{~m}$ (crossed the finish line), Greg ran $72 \%$ of $100 \mathrm{~m}$ or $72 \mathrm{~m}$ in the same amount of time.

When Azarah crossed the finish line, Greg was $100-72=28 \mathrm{~m}$ behind.

ANSWER: (C)