Keiko and Leah run on a track that is $150 \mathrm{~m}$ around. It takes Keiko 120 seconds to run 3 times around the track, and it takes Leah 160 seconds to run 5 times around the track. Who is the faster runner and at approximately what speed does she run?
(A) Keiko, $3.75 \mathrm{~m} / \mathrm{s}$
(D) Leah, $4.69 \mathrm{~m} / \mathrm{s}$
(B) Keiko, $2.4 \mathrm{~m} / \mathrm{s}$
(C) Leah, $3.3 \mathrm{~m} / \mathrm{s}$
Solution 1

Since Keiko takes 120 seconds to run 3 times around the track, then it takes her $\frac{1}{3} \times 120=40$ seconds to run 1 time around the track.

Since Leah takes 160 seconds to run 5 times around the track, then it takes her $\frac{1}{5} \times 160=32$ seconds to run 1 time around the track.

Since Leah takes less time to run around the track than Keiko, then she is the faster runner. Since Leah takes 32 seconds to run the $150 \mathrm{~m}$ around the track, then her speed is $\frac{150 \mathrm{~m}}{32 \mathrm{~s}}=4.6875 \mathrm{~m} / \mathrm{s} \approx 4.69 \mathrm{~m} / \mathrm{s}$.

Therefore, Leah is the faster runner and her speed is approximately $4.69 \mathrm{~m} / \mathrm{s}$.

## Solution 2

In 120 seconds, Keiko runs 3 times around the track, or $3 \times 150=450 \mathrm{~m}$ in total. Therefore, her speed is $\frac{450 \mathrm{~m}}{120 \mathrm{~s}}=3.75 \mathrm{~m} / \mathrm{s}$.

In 160 seconds, Leah runs 5 times around the track, or $5 \times 150=750 \mathrm{~m}$ in total. Therefore, her speed is $\frac{750 \mathrm{~m}}{160 \mathrm{~s}}=4.6875 \mathrm{~m} / \mathrm{s} \approx 4.69 \mathrm{~m} / \mathrm{s}$.

Since Leah's speed is larger, she is the faster runner and her speed is approximately $4.69 \mathrm{~m} / \mathrm{s}$. ANSWER: (D)