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.
Section 6.7 - Rational Equations

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:
Following a severe snowstorm, Ken and Bettina Reeves must clear their driveway and sidewalk. Ken can clear the snow by himself in 4 hours, and Bettina can clear the snow by herself in 6 hours. After Bettina has been working for 3 hours, Ken is able to join her. How much longer will it take them working together to remove the rest of the snow?

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

 1/41/65/12 of a driveway per hour,


 12/5 hours per driveway.

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

 12/5 hours/driveway  1/2 driveway = 6/5 hours.



Go to Math Central