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Anna does sit-ups to get ready for her first triathlon. When she starts, she does a sit-up every seconds. But, as she gets tired, each sit-up takes longer and longer to do.Is the number of sit-ups Anna does proportional to the time she spends doing them?Choose answer:(A) Yes(B) No
Full solution
Q. Anna does sit-ups to get ready for her first triathlon. When she starts, she does a sit-up every seconds. But, as she gets tired, each sit-up takes longer and longer to do.Is the number of sit-ups Anna does proportional to the time she spends doing them?Choose answer:(A) Yes(B) No
- Proportionality Check: To determine if the number of sit-ups is proportional to the time spent, we need to know if the ratio of sit-ups to time is constant. Proportionality implies that as one quantity increases, the other quantity increases at a constant rate.
- Initial Ratio Calculation: Initially, Anna does a sit-up every seconds, which means the ratio is sit-up per seconds. If this ratio were to remain constant, she would do sit-ups in seconds, sit-ups in seconds, and so on.
- Effect of Fatigue: However, the problem states that as Anna gets tired, each sit-up takes longer to do. This means that the time it takes for each subsequent sit-up increases, and therefore, the ratio of sit-ups to time does not remain constant.
- Conclusion: Since the ratio of sit-ups to time is not constant, the number of sit-ups Anna does is not proportional to the time she spends doing them.
