# Problem of the day:

Posted on October 21, 2013

THis problem sounded like the problem other students had been working on, which was  a standard issue “rate together” question in which, to my discerning eye, the middle part wasn’t even necessary.   However, that question had “t” and “t+2,” and then stated that in 5 hours, the fractional part of the job done was 5/t + 5/(t + 3).   I am not sure that the last part was the same… I think it had a different number of hours, or may just have asked how many hours it would take them…

So, first, I told the student “it’s a cut and paste error — don’t bother with it.”  Then… I figured it might be solvable anyway.

I turned this into a rather nasty problem that turned into a cubic equation, and told the student “ask your teacher, and get back to me.”  (Oh, he said it had stumped all the peer tutors, too.)

“One person can clean a house in t hours, while another person needs t + 3 hours.   In 5 hours, the fractional part of the job done is 6/t + 6/(t+3).   Determine how many houses can be cleaned in 8 hours.”

Ignoring the fact taht the problem doesn’t say whether either and/or both folks will be working on it, let’s just assume they both are.   HOw would *you* tackle that problem?

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