Medium1 markMultiple Choice
AQA GCSE · Question 27.2 · Ratio Proportion and Rates of Change
In fact, of the 15 people
6 work at a slower rate
9 work at a faster rate.
What does this mean about the number of hours it will take to complete the job? Tick one box.
In fact, of the 15 people
6 work at a slower rate
9 work at a faster rate.
What does this mean about the number of hours it will take to complete the job? Tick one box.
Answer options:
A.
It is greater than the answer to (a)
B.
It is the same as the answer to (a)
C.
It is less than the answer to (a)
D.
It is not possible to say
How to approach this question
1. The answer in part (a) was based on the assumption that all 15 people work at the same average rate.
2. We are now told that some work slower and some work faster than this average rate.
3. We have 6 people working slower and 9 people working faster.
4. The overall average speed depends on *how much* slower and *how much* faster they work.
5. For example, if the 6 slow workers are only slightly slower, but the 9 fast workers are much faster, the job could be done quicker.
6. Conversely, if the 6 slow workers are very slow, and the 9 fast workers are only slightly faster, the job could take longer.
7. Since we don't know the exact rates, we cannot determine the overall effect on the time taken. Therefore, it is not possible to say.
Full Answer
D.It is not possible to say✓ Correct
It is not possible to say
In part (a), we calculated the time based on the assumption that all 15 people worked at the same, average rate. The result was 6 hours.
Now, this assumption is changed. We have a mixed group:
- 6 people work at a "slower rate".
- 9 people work at a "faster rate".
The key issue is that we don't know the magnitude of these different rates.
- The "slower rate" could be just 1% slower or it could be 90% slower.
- The "faster rate" could be just 1% faster or it could be 200% faster.
Because more people (9) are working faster than are working slower (6), it might seem that the job will be completed more quickly. However, if the 6 "slow" workers are extremely slow, their negative impact on the total work output could outweigh the positive impact of the 9 "fast" workers, even if the fast workers are only slightly faster than average.
Without knowing the specific rates of work for each group, we cannot compare the new average rate to the original average rate. Therefore, **it is not possible to say** how the completion time will be affected.
Common mistakes
✗ Guessing that because more people are faster, the time must be less. This ignores the magnitude of the difference in speeds.
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