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06 Aug 2026, 10:51
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Rina and Maya start at the same time from a trailhead and ride bicycles at their respective constant speeds along the same straight path toward a ranger station 54 miles away, with Rina riding faster than Maya. When Rina reaches the ranger station, she immediately turns around and rides back along the same path until she meets Maya. How many miles has Maya ridden when they meet?
(1) Rina rides 2 times as fast as Maya.
(2) Rina rides 18 miles per hour faster than Maya.
(1) Rina rides 2 times as fast as Maya.
(2) Rina rides 18 miles per hour faster than Maya.
06 Aug 2026, 10:51
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Official Solution:
Rina and Maya start at the same time from a trailhead and ride bicycles at their respective constant speeds along the same straight path toward a ranger station 54 miles away, with Rina riding faster than Maya. When Rina reaches the ranger station, she immediately turns around and rides back along the same path until she meets Maya. How many miles has Maya ridden when they meet?
(1) Rina rides 2 times as fast as Maya.
Since Rina rides 2 times as fast as Maya, by the time they meet, Rina must have ridden 2 times as far as Maya.
Let Maya have ridden \(m\) miles. Rina rides 54 miles to the ranger station and then \(54 - m\) miles back, so Rina’s total distance is:
\(54 + (54 - m) = 108 - m\)
\(108 - m = 2m\)
\(m = 36\)
Sufficient.
(2) Rina rides 18 miles per hour faster than Maya.
This gives only the difference between their speeds, not the ratio.
For example, Rina and Maya could ride at 36 and 18 miles per hour, respectively, or at 54 and 36 miles per hour, respectively. These pairs have different speed ratios and therefore produce different meeting points.
Not sufficient.
Answer: A
Rina and Maya start at the same time from a trailhead and ride bicycles at their respective constant speeds along the same straight path toward a ranger station 54 miles away, with Rina riding faster than Maya. When Rina reaches the ranger station, she immediately turns around and rides back along the same path until she meets Maya. How many miles has Maya ridden when they meet?
(1) Rina rides 2 times as fast as Maya.
Since Rina rides 2 times as fast as Maya, by the time they meet, Rina must have ridden 2 times as far as Maya.
Let Maya have ridden \(m\) miles. Rina rides 54 miles to the ranger station and then \(54 - m\) miles back, so Rina’s total distance is:
\(54 + (54 - m) = 108 - m\)
\(108 - m = 2m\)
\(m = 36\)
Sufficient.
(2) Rina rides 18 miles per hour faster than Maya.
This gives only the difference between their speeds, not the ratio.
For example, Rina and Maya could ride at 36 and 18 miles per hour, respectively, or at 54 and 36 miles per hour, respectively. These pairs have different speed ratios and therefore produce different meeting points.
Not sufficient.
Answer: A
