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Unformatted text preview: hours when they were finally 300 miles apart. Also, even though the problem didn’t ask for it, the second car will have traveled for 8.09998 hours before they are 300 miles apart. Notice as well that this is NOT the second solution without the negative this time, unlike the first example. Example 3 An office has two envelope stuffing machines. Working together they can stuff a batch of envelopes in 2 hours. Working separately it will take the second machine 1 hour longer than the first machine to stuff a batch of envelopes. How long would it take each machine do stuff a batch of envelopes by themselves? Solution Let t be the amount of time it takes the first machine (Machine A) to stuff a batch of envelopes by itself. That means that it will take the second machine (Machine B) t + 1 hours to stuff a batch of envelopes by itself. The word equation for this problem is then, æ Portion of job ö æ Portion of job ö ç ÷+ç ÷ = 1 Job è done by Machine A ø è done by Machine B ø æ Work Rate öæ Time Spent ö æ Work Rate öæ Time Spent ö ç ÷ç ÷+ç ÷ç ÷ =1 è of Machine A øè Working ø è of Machine B øè Working ø We know the time spent working together (2 h...
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