Getting the Job Done
Date: 12/17/96 at 14:59:02 From: Jerrad Evans Subject: Solving a problem Our teacher gave us a worksheet with a question on it that I don't seem to be able to solve. I've tried to make some equations out of it, but there doesn't seem to be one (at least nothing that I can see): Two typists share a job. The second typist begins working one hour after the first. Three hours after the first typist has begun working, only 11/20 of the job has been completed. When the job is finished, it turns out that each typist has done exactly half of the work. How many hours would it take each typist, working alone, to complete the job? Could you help? Thanks! Jerrad Evans
Date: 12/17/96 at 18:58:39 From: Doctor Wilkinson Subject: Re: Solving a problem What you're really being asked is how fast each typist types. That is, to answer the question "how long would this typist take to finish this job working alone" you need to know how much of this job the typist would get done in an hour. For example, if he or she takes 4 hours to finish the job, then in 1 hour he or she finishes 1/4 of the job. These rates are easier to work with than the times. In most problems involving time, you may want to move back and forth between looking at rates and looking at periods of time. After that introduction, let's let: a = amount of job first typist can do in an hour b = amount of job second typist can do in an hour Another number we don't know is T, the number of hours the typists took to finish the job. So we've got three unknowns, and we're going to need three equations. Do we have three pieces of information we can get equations out of? We have the curious piece of information that the first typist started an hour ahead of the second typist. What this means is that after t hours, where t is at least 1, the amount that has been done by the first typist is (at), and the amount that has been done by the second typist is b(t-1), because the second typist has worked an hour less than the first. The next thing we know is that after three hours, 11/20 of the job has been done. At that time the first typist has done an amount 3a and the second typist has done an amount 2b, so the total is 3a + 2b = 11/20 That's one equation. Two more to go! We're also given that when the job is finished, each typist has done exactly half of it. So this involves our unknown time T, the time to finish the job. The first typist has done half of it, so aT = 1/2 and the second typist has also done half of it, so b(T-1) = 1/2. And there we have the three equations. -Doctor Wilkinson, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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