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30 May 2026, 08:59
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Rina commutes between her apartment and her office in one of two ways: she can bike to the office and back along the Greenway Trail at a constant speed, or she can take the shuttle to the office and back along the Cityline Route at a constant speed. How many minutes does it take Rina to bike from her apartment to her office?
(1) When Rina bikes from her apartment to her office and then takes the shuttle back to her apartment, the total distance she travels is 7 kilometers, and her average (arithmetic mean) speed for that entire trip is 30 kilometers per hour.
(2) When Rina takes the shuttle from her apartment to her office and then takes the shuttle back to her apartment, the total distance she travels is 8 kilometers, and her average (arithmetic mean) speed for that entire trip is 40 kilometers per hour.
(1) When Rina bikes from her apartment to her office and then takes the shuttle back to her apartment, the total distance she travels is 7 kilometers, and her average (arithmetic mean) speed for that entire trip is 30 kilometers per hour.
(2) When Rina takes the shuttle from her apartment to her office and then takes the shuttle back to her apartment, the total distance she travels is 8 kilometers, and her average (arithmetic mean) speed for that entire trip is 40 kilometers per hour.
30 May 2026, 08:59
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Official Solution:
Rina commutes between her apartment and her office in one of two ways: she can bike to the office and back along the Greenway Trail at a constant speed, or she can take the shuttle to the office and back along the Cityline Route at a constant speed. How many minutes does it take Rina to bike from her apartment to her office?
(1) When Rina bikes from her apartment to her office and then takes the shuttle back to her apartment, the total distance she travels is 7 kilometers, and her average (arithmetic mean) speed for that entire trip is 30 kilometers per hour.
The total time for that trip is \(\frac{7}{30}\) hours = 14 minutes. This tells us (bike time one way) + (shuttle time one way) = 14 minutes, but it does not give either time by itself. Not sufficient.
(2) When Rina takes the shuttle from her apartment to her office and then takes the shuttle back to her apartment, the total distance she travels is 8 kilometers, and her average (arithmetic mean) speed for that entire trip is 40 kilometers per hour.
The total time for the shuttle round trip is \(\frac{8}{40}\) hours = \(\frac{1}{5}\) hour = 12 minutes, so the one way shuttle time is 6 minutes. We still do not know the bike time. Not sufficient.
(1)+(2) From (1), (bike time one way) + (shuttle time one way) = 14 minutes. From (2), shuttle time one way = 6 minutes. So bike time one way = 14 - 6 = 8 minutes. Sufficient.
Answer: C
Rina commutes between her apartment and her office in one of two ways: she can bike to the office and back along the Greenway Trail at a constant speed, or she can take the shuttle to the office and back along the Cityline Route at a constant speed. How many minutes does it take Rina to bike from her apartment to her office?
(1) When Rina bikes from her apartment to her office and then takes the shuttle back to her apartment, the total distance she travels is 7 kilometers, and her average (arithmetic mean) speed for that entire trip is 30 kilometers per hour.
The total time for that trip is \(\frac{7}{30}\) hours = 14 minutes. This tells us (bike time one way) + (shuttle time one way) = 14 minutes, but it does not give either time by itself. Not sufficient.
(2) When Rina takes the shuttle from her apartment to her office and then takes the shuttle back to her apartment, the total distance she travels is 8 kilometers, and her average (arithmetic mean) speed for that entire trip is 40 kilometers per hour.
The total time for the shuttle round trip is \(\frac{8}{40}\) hours = \(\frac{1}{5}\) hour = 12 minutes, so the one way shuttle time is 6 minutes. We still do not know the bike time. Not sufficient.
(1)+(2) From (1), (bike time one way) + (shuttle time one way) = 14 minutes. From (2), shuttle time one way = 6 minutes. So bike time one way = 14 - 6 = 8 minutes. Sufficient.
Answer: C
