SOLUTION: Hi, I would like to just say thank you for taking the time to answer my question. My question is: A laborer built 35 m of stone wall. if she has built 2 m less each day,

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Hi, I would like to just say thank you for taking the time to answer my question. My question is: A laborer built 35 m of stone wall. if she has built 2 m less each day,       Log On


   



Question 1011087: Hi,
I would like to just say thank you for taking the time to answer my question.
My question is:

A laborer built 35 m of stone wall. if she has built 2 m less each day, it would have taken her 2 days longer. How many meters did she build each day, working at her usual rate?
Thank you

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Uniform rates, doing a job, doing a task,
RT=J, one job is "Build wall". Better, J is for "how much wall". The rule stated relates rate, time, amount of job. The attention is given to length of wall, so that is really the meaning of J.
            rate     time     wall length
DONE        r        t        35
IF          r-2      t+2      35

The table of data should make sense, otherwise, that is what help you first need.

Goal is to solve for r, the rate of the work as done. Another unknown variable is t, but the question does not ask for it. You have this system of equations:

system%28rt=35%2C%28r-2%29%28t%2B2%29=35%29

Start with the IF equation.
rt-2t%2B2r-4=35
substitute using the DONE equation,
35-2t%2B2r-4=35
-2t%2B2r-4=0
2r-4=2t
t=r-2, probably only coincidence that it resembles what is seen in the data table.

Back to the DONE equation again,
substitute for t.
rt=35
r%28r-2%29=35
r%5E2-2r-35=0
%28r-7%29%28r%2B5%29=0

The meaningful result is highlight%28r=7%29, meters of wall per day.