Quandaries
and Queries 

My name is Patricia The level is middle school algebra I am the parent. I am homeshooling my son this year. I have the teachers edition, he
has the students. The book is Elementary Algebra for College Students,
6th Edition by Allen R. Angel. Problem #35. We do not get the answer posted in the solutions and teacher's book because our initial equation is not what the solution shows. Here is the problem: We thought the initial equation would be (t+3)/6 + t/4 = 1 where t = time and 1/6 is the rate that Bettina works and 1/4 is the rate that Ken works. The answer in the solution book is t/6+ (t+3)/4 = 1. We don't understand why they add 3 to Ken's rate instead of Bettina's. Can you please explain? We're wondering if the book's solution is perhaps incorrect. Thank you 

Hi Patricia, I get the same answer as you, 6/5 of an hour, or 1 hour and 12 minutes. You asked why the authors "add 3 to Ken's rate instead of Bettina's". You actually added 3 to Betina's time, not her rate. Your variable t measures time in hours, starting when Ken arrives, so the time Bettina works is 3+t hours. I wouldn't have solved this problem using albebra at all. Ken works at the rate of ^{1}/_{4} of a driveway per hour and Betina works at the rate of ^{1}/_{6} of a driveway per hour. Thus, working together they work at the rate of
or
Betina has been working for 3 hours and hence half of the driveway remains to be cleared. Thus the time need to complete the job is
Penny 

