A primary school teacher wants to arrange a visit to a museum.
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A primary school teacher wants to arrange a visit to a museum. The bus driver ensures that the bus starts with a full tank of gas. However, the driver does not remember the fuel tank capacity or fuel efficiency of the engine.
Which of the following statements is/are sufficient to determine if the bus has enough gas to complete the journey?
- Statement 1: The driver drives at a constant speed.
- Statement 2: The driver realizes that three-quarters of the full tank of gas remains after driving 150 miles.
- Statement 3: The driver realizes that three-quarters of the full tank of gas remains after driving 450 miles.
Show answer & explanation
To determine if the bus has enough gas for the journey, one must know the total distance of the journey. None of the provided statements provide the total distance required to reach the museum, making it impossible to conclude if the remaining fuel is sufficient.
Step-by-step Derivation:
Step 1: Identify the goal. The goal is to determine if the bus has enough gas to complete the journey. This requires knowing the total distance of the journey (D_total) and the total range of the bus on a full tank (R_max).
Step 2: Analyze Statement 1. 'The driver drives at a constant speed.' This provides information about velocity, but does not provide fuel capacity, fuel efficiency, or the distance to the destination. It is insufficient.
Step 3: Analyze Statement 2. 'Three-quarters of the full tank remains after driving 150 miles.' This means 1/4 of the tank was used for 150 miles. Therefore, the total range (R_max) = 150 * 4 = 600 miles. While we now know the bus can travel 600 miles on a full tank, we still do not know the distance to the museum (D_total). Without D_total, we cannot determine if 600 miles is enough.
Step 4: Analyze Statement 3. 'Three-quarters of the full tank remains after driving 450 miles.' This means 1/4 of the tank was used for 450 miles. Therefore, the total range (R_max) = 450 * 4 = 1800 miles. Again, while we know the total range, we do not know the distance to the museum (D_total).
Step 5: Conclusion. Since the distance to the museum is not provided in any statement, no combination of statements allows us to determine if the fuel is sufficient for the specific journey.