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06 Aug 2026, 08:01
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If Lena, Marco, and Oliver took turns paddling a canoe for the entire 1,120-meter route from East Dock to Pine Landing, with exactly one person paddling at a time, who paddled the greatest distance?
(1) Lena paddled 2 hours longer than Marco, and their average (arithmetic mean) speeds were 70 meters per hour and 50 meters per hour, respectively.
(2) Oliver paddled for 10 hours at an average (arithmetic mean) speed of 50 meters per hour.
(1) Lena paddled 2 hours longer than Marco, and their average (arithmetic mean) speeds were 70 meters per hour and 50 meters per hour, respectively.
(2) Oliver paddled for 10 hours at an average (arithmetic mean) speed of 50 meters per hour.
06 Aug 2026, 08:01
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Official Solution:
If Lena, Marco, and Oliver took turns paddling a canoe for the entire 1,120-meter route from East Dock to Pine Landing, with exactly one person paddling at a time, who paddled the greatest distance?
(1) Lena paddled 2 hours longer than Marco, and their average speeds were 70 meters per hour and 50 meters per hour, respectively.
Let \(m\) be the number of hours Marco paddled. So:
• Marco’s distance \(= 50m\)
• Lena’s distance \(= 70(m + 2)\)
But Oliver’s distance is not fixed because \(m\) is not fixed.
Not sufficient.
(2) Oliver paddled for 10 hours at an average speed of 50 meters per hour.
So Oliver paddled:
\(10 * 50 = 500\) meters
But we do not know how Lena and Marco split the remaining 620 meters.
Not sufficient.
(1)+(2) From statement (2), Oliver paddled 500 meters. So Lena and Marco together paddled:
\(1,120 - 500 = 620\) meters
From statement (1):
• Marco’s distance \(= 50m\)
• Lena’s distance \(= 70(m + 2)\)
So:
\(50m + 70(m + 2) = 620\)
\(m = 4\)
Therefore:
• Marco’s distance \(= 50 * 4 = 200\) meters
• Lena’s distance \(= 70 * 6 = 420\) meters
• Oliver’s distance \(= 500\) meters
So Oliver paddled the greatest distance.
Sufficient.
Answer: C
If Lena, Marco, and Oliver took turns paddling a canoe for the entire 1,120-meter route from East Dock to Pine Landing, with exactly one person paddling at a time, who paddled the greatest distance?
(1) Lena paddled 2 hours longer than Marco, and their average speeds were 70 meters per hour and 50 meters per hour, respectively.
Let \(m\) be the number of hours Marco paddled. So:
• Marco’s distance \(= 50m\)
• Lena’s distance \(= 70(m + 2)\)
But Oliver’s distance is not fixed because \(m\) is not fixed.
Not sufficient.
(2) Oliver paddled for 10 hours at an average speed of 50 meters per hour.
So Oliver paddled:
\(10 * 50 = 500\) meters
But we do not know how Lena and Marco split the remaining 620 meters.
Not sufficient.
(1)+(2) From statement (2), Oliver paddled 500 meters. So Lena and Marco together paddled:
\(1,120 - 500 = 620\) meters
From statement (1):
• Marco’s distance \(= 50m\)
• Lena’s distance \(= 70(m + 2)\)
So:
\(50m + 70(m + 2) = 620\)
\(m = 4\)
Therefore:
• Marco’s distance \(= 50 * 4 = 200\) meters
• Lena’s distance \(= 70 * 6 = 420\) meters
• Oliver’s distance \(= 500\) meters
So Oliver paddled the greatest distance.
Sufficient.
Answer: C
