Question

Brandon and Chris together can do a piece of work in 12 days. After Brandon has worked alone for 5 days, Chris finishes the work alone in 26 days. In what time can each alone do the work?

Answer 1

we need some variables, two actually
we can call bradon's rate \(x\) and chris's rate \(y\)
then there combined rate is \(x+y\) and you know that they can complete one job in 12 days so we have one equation, namely
\[12(x+y)=1\]

Answer 2

the second thing we know is that
\[5x+26y=1\] so we have two equations with two unknowns,
\[12x+12y=1\]\[2x+26y=1\] and we can solve that system of equations for \(x\) and \(y\)

Answer 3

sure did didn't i?
glad you are here to keep me honest

Answer 4

lets try
\[12x+12y=1\]
\[5x+26y=1\] maybe that will work better
@hero do you have a better method? this is kind of clunky

Answer 5

so i have to find solution to x and y now?

Answer 6

ack, too bad, i hate these fractions
at any rate solving gives \(x=\frac{1}{18}\) and \(y=\frac{1}{26}\) so brandon can do it in 18 hours and slow poke chris takes 36 hours

Answer 7

another typo
\(y=\frac{1}{36}\)
i bet there is a snappier way

Answer 8

@lynn17 yes you have to solve the two equations
multiply the first one by 5, the second one by -12 and add, the \(x\) will drop out

Answer 9

yeah other ways are just as messy, actually more so

Answer 10

ok thank you

Answer 11

how did you get from the fractions to the solution?

Answer 12

from fractions to solutions
if \(x=\frac{1}{18}\) then the rate is \(\frac{1}{18}\) i.e. you can do \(\frac{1}{18}\) of the job in one hour
therefore it takes you 18 hours to do the job
i.e. take the reciprocal