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Lucas can process four times as many data files per day as Martin. Consequently, Lucas takes 30 days fewer than Martin to complete a large data-processing task. If Lucas and Martin work together, how many days will they take to complete the task?
A. 7
B. 8
C. 9
D. 10
E. 12
A. 7
B. 8
C. 9
D. 10
E. 12
10 Mar 2026, 22:37
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Official Solution:
Lucas can process four times as many data files per day as Martin. Consequently, Lucas takes 30 days fewer than Martin to complete a large data-processing task. If Lucas and Martin work together, how many days will they take to complete the task?
A. 7
B. 8
C. 9
D. 10
E. 12
Let Martin’s rate \(= r\) per day, Lucas’s rate \(= 4r\) per day. Total work \(= T\).
Martin time \(= \frac{T}{r}\).
Lucas time \(= \frac{T}{4r}\).
Given:
\(\frac{T}{r} - \frac{T}{4r} = 30\).
\(\frac{T}{r} * (1 - \frac{1}{4}) = 30\).
\(\frac{T}{r} = 40\).
Combined rate \(= r + 4r = 5r\).
Time it takes to complete the task together \(= \frac{T}{5r} = \frac{(T/r)}{5} = \frac{40}{5} = 8\).
Answer: B
Lucas can process four times as many data files per day as Martin. Consequently, Lucas takes 30 days fewer than Martin to complete a large data-processing task. If Lucas and Martin work together, how many days will they take to complete the task?
A. 7
B. 8
C. 9
D. 10
E. 12
Let Martin’s rate \(= r\) per day, Lucas’s rate \(= 4r\) per day. Total work \(= T\).
Martin time \(= \frac{T}{r}\).
Lucas time \(= \frac{T}{4r}\).
Given:
\(\frac{T}{r} - \frac{T}{4r} = 30\).
\(\frac{T}{r} * (1 - \frac{1}{4}) = 30\).
\(\frac{T}{r} = 40\).
Combined rate \(= r + 4r = 5r\).
Time it takes to complete the task together \(= \frac{T}{5r} = \frac{(T/r)}{5} = \frac{40}{5} = 8\).
Answer: B
