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06 Feb 2026, 05:01
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
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Question Stats:
65% (02:03) correct
35%
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wrong
based on 131
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A teacher corrected the first half of a stack of exams at a rate of 9 exams per hour and the second half of the stack at a rate of 18 exams per hour. If it took her 4 hours to correct all of the exams, how many exams were in the stack?
A. 48
B. 50
C. 52
D. 54
E. 56
A. 48
B. 50
C. 52
D. 54
E. 56
06 Feb 2026, 06:05
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So first half is marked at 9 eph (exams per hour) second half at 18 eph.
Since the rate doubles from 9 -> 18, the time taken to complete the same of work is halved. (we know the work is the same amount as they each perform 1/2).
So when working at 18 eph is takes 1T of time to complete half, and when working at 9 eph it takes 2T to complete a half. So total time takes 3T
work done = rate x time
This means the total work done (D) = 18T + 9(2T)
4 hours total divided by 3T means T=4/3 hours
18(4/3) + 9 x 2 x(4/3) = 48
Since the rate doubles from 9 -> 18, the time taken to complete the same of work is halved. (we know the work is the same amount as they each perform 1/2).
So when working at 18 eph is takes 1T of time to complete half, and when working at 9 eph it takes 2T to complete a half. So total time takes 3T
work done = rate x time
This means the total work done (D) = 18T + 9(2T)
4 hours total divided by 3T means T=4/3 hours
18(4/3) + 9 x 2 x(4/3) = 48
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06 Feb 2026, 08:36
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By applying the matrix approach, we can get an answer
As we know
\(\frac{E}{9} \)+ \(\frac{E}{18} \)= 4(total time mentioned in the question)
E= 24
Total Exams = 24 +24 = 48
Answer: A
| Rate | Time | Exam | |
| First half | 9 | E/9 | E |
| Second half | 18 | E/18 | E |
As we know
\(\frac{E}{9} \)+ \(\frac{E}{18} \)= 4(total time mentioned in the question)
E= 24
Total Exams = 24 +24 = 48
Answer: A
kevincan
