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16 Jul 2003, 14:18
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Two people, each working at the same constant rate, can build three widgets in four hours. How long will it take 100 people each working at that same rate to build 100 widgets?
(A) 200 hours
(B) 66 2/3 hours
(C) 16 2/3 hours
(D) 3 1/3 hours
(E) 2 2/3 hours
Variation (if you can do part 1 you can do this in your head):
Seven people, each working at the same constant rate, can build seven widgets in seven hours. How long will it take 100 people each working at that same rate to build 50 widgets?
(A) 100 hours
(B) 50 hours
(C) 14 2/7 hours
(D) 7 hours
(E) 3 1/2 hours
(A) 200 hours
(B) 66 2/3 hours
(C) 16 2/3 hours
(D) 3 1/3 hours
(E) 2 2/3 hours
Variation (if you can do part 1 you can do this in your head):
Seven people, each working at the same constant rate, can build seven widgets in seven hours. How long will it take 100 people each working at that same rate to build 50 widgets?
(A) 100 hours
(B) 50 hours
(C) 14 2/7 hours
(D) 7 hours
(E) 3 1/2 hours
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16 Jul 2003, 22:22
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The correct answer is (E). The key to solving this type of problem is to determine the rate that each individual can work, then carry over that rate to the new situation. The тАЬteamтАЭ can build three widgets in four hours. Hence, the rate that the team can build the widgets is 3/4 widgets per hour. Since the team rate is equal to the sum of the individual rates of each member of the team and there are two people on the team each working at the same rate, each person can work at a rate of (3/4)/2 or 3/8 widgets per hour.
There is an alternative way to calculate the individual rate. It is reasonable to assume that multiple people working at the same rate to build multiple widgets would each build an equal number of widgets. Hence, the number of widgets each person builds is equal to the number of total widgets divided by the number of people or, in this case, 3/2 widgets. Since everyone works simultaneously over the whole four hours, each person builds his or her allotment of widgets over four hours also. Since Rate = Work/Time, the individual rate for each person is (3/2 widgets)/(4 hours) = 3/8 widgets per hour, which agrees with the first method.
Now we have 100 people each working at the individual rate of 3/8 widgets per hour. It follows that the combined rate of the team of 100 people is 100(3/8) or 300/8 widgets per hour. There are 100 widgets to build. Since Time = Work/Rate, the time needed to build 100 widgets at the rate of 300/8 widgets per hour is 100/(300/8) = 800/300 = 8/3 = 2 2/3 hours and the correct answer choice is (E).
If you understand the concept in the above method, you can solve the variation in your head. If seven people can build seven widgets in seven hours, each person needs seven hours to create one widget. For 100 people to build 50 widgets, each person only has to build 1/2 of a widget, so the total time for all 100 people working simultaneously to build 1/2 widget each is 1/2 of seven hours, or 3 1/2 hours and the correct answer is also (E).
There is an alternative way to calculate the individual rate. It is reasonable to assume that multiple people working at the same rate to build multiple widgets would each build an equal number of widgets. Hence, the number of widgets each person builds is equal to the number of total widgets divided by the number of people or, in this case, 3/2 widgets. Since everyone works simultaneously over the whole four hours, each person builds his or her allotment of widgets over four hours also. Since Rate = Work/Time, the individual rate for each person is (3/2 widgets)/(4 hours) = 3/8 widgets per hour, which agrees with the first method.
Now we have 100 people each working at the individual rate of 3/8 widgets per hour. It follows that the combined rate of the team of 100 people is 100(3/8) or 300/8 widgets per hour. There are 100 widgets to build. Since Time = Work/Rate, the time needed to build 100 widgets at the rate of 300/8 widgets per hour is 100/(300/8) = 800/300 = 8/3 = 2 2/3 hours and the correct answer choice is (E).
If you understand the concept in the above method, you can solve the variation in your head. If seven people can build seven widgets in seven hours, each person needs seven hours to create one widget. For 100 people to build 50 widgets, each person only has to build 1/2 of a widget, so the total time for all 100 people working simultaneously to build 1/2 widget each is 1/2 of seven hours, or 3 1/2 hours and the correct answer is also (E).
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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