20 hours is the value you get if you directly apply the expression that appears in the latter half of the question, “the amount Mr. A and Mr. B can complete together in one hour is 1/36 + 1/45”. Since 1/36+1/45=5/180+4/180=9/180=1/20, two people working together could indeed finish one week of work in 20 hours. However, this question is set up so that Mr. B handles Monday alone and Mr. A handles Tuesday onward alone; there is no point at which the two work at the same time. This is not a situation for the joint-work formula, so it is wrong.
×Incorrectイ
25 hours is about 4.6 hours shorter than the correct value of 29.6 hours, so it does not fit. This value tends to come from an error such as using the ratio in the wrong direction when converting Mr. B's 8 hours on Monday into Mr. A's working time: treating the progress as 8×(45/36)=10 hours and computing 36−10=26 hours (≈25). The correct conversion goes the other way: Mr. B's 8 hours amount to a workload of 8/45, and converting that into Mr. A's time gives only (8/45)×36=6.4 hours. Hence 36−6.4=29.6 hours. The right direction of thinking is that one day of work by the slower Mr. B does not reach the output of one day of work by the faster Mr. A.
○ウ
正解The correct answer is ウ (30 hours). The standard approach for this type of problem is to set the workload of one week to 1 and think in terms of the amount of work done per hour. As the question states, the amount Mr. A can complete in one hour is 1/36, and Mr. B 1/45 (because working alone they need 36 hours and 45 hours respectively to finish one week of work). First, find the portion Mr. B handled on Monday. The working time per day is 8 hours, so the workload Mr. B finished is 8×(1/45)=8/45. Therefore the workload remaining from Tuesday onward is 1−8/45=37/45. Since Mr. A processes this alone, the time needed is remaining workload ÷ Mr. A's work per hour = (37/45)÷(1/36)=37×36/45=1332/45=29.6 hours. The closest choice to this is 30 hours. As a check, the remaining 4 days from Tuesday to Friday provide 4×8=32 hours, so with 29.6 hours the shipping can be finished within the week, which does not conflict with the condition that the previous week's orders must be shipped by the end of the following week.
×Incorrectエ
35 hours is exactly the value obtained when the roles of Mr. A and Mr. B are mixed up. If Mr. A had handled Monday, the workload completed would be 8×(1/36)=8/36, leaving 28/36=7/9. Processing that with Mr. B would take 45×(7/9)=35 hours. However, in this question it is Mr. B who handled Monday, and Mr. A who handles Tuesday onward. To avoid mixing up who worked at which speed and for how many hours, you must always check the correspondence between the person in charge and the average working time.
ここがポイント
This is the basic form of a work-rate problem. Set the total workload to 1; for a person who needs T hours to finish it alone, the amount of work done in one hour is 1/T. If that person works for t hours, t/T of the work is done, and dividing the remaining workload by another person's work per hour gives the time that person needs. In this question Mr. B finishes 8/45, and Mr. A processes the remaining 37/45 at a rate of 1/36, giving (37/45)÷(1/36)=29.6 hours.
Not mixing up the numbers given in the conditions is what decides whether you score. Keep in mind the premises that the working time is 8 hours per day and the working days are the 5 days from Monday to Friday (40 hours per week), and check the correspondence between the person in charge and the average working time (A = 36 hours, B = 45 hours). Verifying whether your answer fits within the time available in the remaining days (32 hours from Tuesday to Friday) lets you notice a mix-up or a calculation mistake.