386390 wrote:
Bob and Alice can finish a job together in 3 hours. If Bob can do the job by himself in 5 hours, what percent of the job does Alice do?
A) 10
B) 20
C) 40
D) 50
E) 60
Since Bob and Alice can complete a job in 3 hours, the combined rate of Bob and Alice = 1/3. Since Bob can do the job by himself in 5 hours, his rate is 1/5.
Thus, the rate of Alice is 1/3 - 1/5 = 5/15 - 3/15 = 2/15.
Thus, when working together, the combined work is 1/3 and Alice's work is 2/15.
Since Alice has worked for 3 hours, her work is 3 x 2/15 = 2/5. Furthermore, since we consider the complete job the number 1, the percentage of the job done by Alice is:
(2/5)/1 = 2/5 = 40%
Answer: C
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