LulaBrazilia wrote:On Monday morning a certain machine ran continuously at a uniform rate to fill a production order. At what time did it completely fill the order that morning?
1) The machine began filling the order at 9:30 am
2) The machine had filled 1/2 of the order by 10:30am and 5/6 of the order by 11:10am
We are given that a certain machine ran continuously at uniform rate to fill a production order. We need to determine at what time it filled the order.
Statement One Alone:
The machine began filling the order at 9:30 a.m.
Only knowing what time the machine began filling the order is not enough information to determine at what time the order was completely filled. Statement one alone is not sufficient to answer the question.
Statement Two Alone:
The machine had filled 1/2 of the order by 10:30 a.m. and 5/6 of the order by 11:10 a.m.
Using the information in statement two, we can determine that the machine completed 5/6 - 1/2 = 5/6 - 3/6 = 2/6 = 1/3 of the job in 40 minutes. Since rate = work/time, the rate of the machine is (1/3)/40 = 1/120. We can now determine how many minutes it would take the machine to complete the remaining 1/6 of the job.
time = work/rate
time = (1/6)/(1/120) = 120/6 = 20 minutes.
Thus, the machine needs 20 more minutes to complete the remaining 1/6 of the job. That is, the machine completes the entire job at 11:30 a.m.
Answer:
B
