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07 Aug 2025, 05:55
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In a hot dog eating contest, two participants, Leo and Marco, competed for the same amount of time. During that time, Leo ate 36 hot dogs, and Marco ate 30 hot dogs. What was Marco’s average rate, in hot dogs per hour, during that time?
(1) Marco’s average rate was 6 hot dogs per hour less than Leo’s.
(2) In the first 20 minutes, Leo ate 12 hot dogs.
(1) Marco’s average rate was 6 hot dogs per hour less than Leo’s.
(2) In the first 20 minutes, Leo ate 12 hot dogs.
07 Aug 2025, 05:55
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Official Solution:
In a hot dog eating contest, two participants, Leo and Marco, competed for the same amount of time. During that time, Leo ate 36 hot dogs, and Marco ate 30 hot dogs. What was Marco’s average rate, in hot dogs per hour, during that time?
(1) Marco’s average rate was 6 hot dogs per hour less than Leo’s.
Assuming Marco’s average rate was \(x\) hot dogs per hour, Leo's rate would be \(x + 6\) hot dogs per hour. Since they competed for the same amount of time, we can equate by time: \(\frac{36}{x + 6} = \frac{30}{x}\). Solving this gives \(x = 30\) hot dogs per hour. Sufficient.
(2) In the first 20 minutes, Leo ate 12 hot dogs.
This implies that Leo's average rate for the first 20 minutes was 36 hot dogs per hour. However, we cannot assume that Leo maintained the same rate while eating the remaining 36 - 12 = 24 hot dogs. He could have eaten those in 1 hour or in 10 hours, resulting in different total durations and, therefore, different rates for Marco. Not sufficient.
Answer: A
In a hot dog eating contest, two participants, Leo and Marco, competed for the same amount of time. During that time, Leo ate 36 hot dogs, and Marco ate 30 hot dogs. What was Marco’s average rate, in hot dogs per hour, during that time?
(1) Marco’s average rate was 6 hot dogs per hour less than Leo’s.
Assuming Marco’s average rate was \(x\) hot dogs per hour, Leo's rate would be \(x + 6\) hot dogs per hour. Since they competed for the same amount of time, we can equate by time: \(\frac{36}{x + 6} = \frac{30}{x}\). Solving this gives \(x = 30\) hot dogs per hour. Sufficient.
(2) In the first 20 minutes, Leo ate 12 hot dogs.
This implies that Leo's average rate for the first 20 minutes was 36 hot dogs per hour. However, we cannot assume that Leo maintained the same rate while eating the remaining 36 - 12 = 24 hot dogs. He could have eaten those in 1 hour or in 10 hours, resulting in different total durations and, therefore, different rates for Marco. Not sufficient.
Answer: A
05 Sep 2025, 09:56
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I like the solution - it’s helpful.
