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
Patricia
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
1/4 + 1/6 = 5/12 of a driveway per hour,
or
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.
Penny