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12 Jan 2026, 07:43
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A farmer worked on clearing a field over two days. On the second day, the farmer’s rate was 8 square meters per hour less than on the first day. Over the two days together, the farmer cleared 240 square meters in 14 hours of work. Which of the following could be the farmer’s rate, in square meters per hour, on the second day?
I. 9
II. 14
III. 19
A. I only
B. II only
C. III only
D. I and II only
E. II and III only
I. 9
II. 14
III. 19
A. I only
B. II only
C. III only
D. I and II only
E. II and III only
12 Jan 2026, 07:43
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Bookmarks
Official Solution:
A farmer worked on clearing a field over two days. On the second day, the farmer’s rate was 8 square meters per hour less than on the first day. Over the two days together, the farmer cleared 240 square meters in 14 hours of work. Which of the following could be the farmer’s rate, in square meters per hour, on the second day?
I. 9
II. 14
III. 19
A. I only
B. II only
C. III only
D. I and II only
E. II and III only
The average rate over the two days is \(\frac{240}{14} ≈ 17.1\). An average must lie between the individual rates. If the rate on the second day was \(r\) and the rate on the first day was \(r + 8\), then the average of 17.1 must satisfy \(r < 17.1 < r + 8\).
Now let's check the options:
I. 9
If \(r = 9\), then \(r + 8 = 17\). Both rates (9 and 17) are below the average of 17.1, which is not possible.
II: 14
If \(r = 14\), then \(r + 8 = 22\). The average of 17.1 lies between 14 and 22, so this is possible.
III: 19
If \(r = 19\), then \(r + 8 = 27\). Both rates (19 and 27) are above the average of 17.1, which is not possible.
Answer: B
A farmer worked on clearing a field over two days. On the second day, the farmer’s rate was 8 square meters per hour less than on the first day. Over the two days together, the farmer cleared 240 square meters in 14 hours of work. Which of the following could be the farmer’s rate, in square meters per hour, on the second day?
I. 9
II. 14
III. 19
A. I only
B. II only
C. III only
D. I and II only
E. II and III only
The average rate over the two days is \(\frac{240}{14} ≈ 17.1\). An average must lie between the individual rates. If the rate on the second day was \(r\) and the rate on the first day was \(r + 8\), then the average of 17.1 must satisfy \(r < 17.1 < r + 8\).
Now let's check the options:
I. 9
If \(r = 9\), then \(r + 8 = 17\). Both rates (9 and 17) are below the average of 17.1, which is not possible.
II: 14
If \(r = 14\), then \(r + 8 = 22\). The average of 17.1 lies between 14 and 22, so this is possible.
III: 19
If \(r = 19\), then \(r + 8 = 27\). Both rates (19 and 27) are above the average of 17.1, which is not possible.
Answer: B
