What do you think? Justify your answer.
Understand the Problem
The question is asking to evaluate Zara's reasoning about how the time it takes for a train journey changes when the number of people doubles. We need to determine if Zara's logic is correct and justify our answer.
Answer
Zara is incorrect. The train journey will still take 20 minutes.
Answer for screen readers
Zara is incorrect. The time taken for the train journey should not change with the number of people on the train. Therefore, the train journey will still take 20 minutes.
Steps to Solve
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Identify the relationship between the number of people and the time The problem states that 80 people take 20 minutes. We need to determine if adding more people to the train will increase the travel time.
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Analyze the relationship The number of passengers on the train does not affect the travel time. The train will still take the same amount of time to complete the journey regardless of whether it is full or empty.
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Evaluate Zara's reasoning Zara's reasoning is incorrect because she assumes that doubling the number of people will double the travel time. This is not the case, as the travel time remains constant regardless of the number of people on the train. Her statement "60 x 2 = 120, so 20 x 2 = 40 minutes" is mathematically correct but logically flawed in this context. According to Zara, 80 people = 20 minutes, therefore 160 people = 40 minutes. To get 160 people she multiplies 80 people by 2, so she doubles the amount of people.
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Provide a correct justification The travel time will remain at 20 minutes, since the number of people on the train does not affect the travel time.
Zara is incorrect. The time taken for the train journey should not change with the number of people on the train. Therefore, the train journey will still take 20 minutes.
More Information
The number of people on a train typically doesn't affect the travel time unless the weight causes the train to slow down, but for normal passenger numbers this is not a factor.
Tips
A common mistake would be for people to assume that the time will increase slightly because of extra weight, or believe that this problem relates to resource allocation and time. These are invalid
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