SOLUTION: Melissa can do 2 jobs in 3 hours; when Krista helps, together they manage to do 8 jobs in 3 hours. How long would it take Krista to do 1 job? I have not done a problem like t

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Melissa can do 2 jobs in 3 hours; when Krista helps, together they manage to do 8 jobs in 3 hours. How long would it take Krista to do 1 job? I have not done a problem like t      Log On


   



Question 1067976: Melissa can do 2 jobs in 3 hours; when Krista helps, together they manage to do 8 jobs in 3 hours. How long would it take Krista to do 1 job?

I have not done a problem like this in a while, and I cannot locate past notes on how to solve it. Any sort of assistance would be awesome, thank you!

Found 3 solutions by josmiceli, rothauserc, ikleyn:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their individual rates of working to
get their rate working together
Let +t+ = Krista's time in hrs to do 1 job
----------------------------------------
Melissa's rate of working:
[ 2 jobs ] / [ 3 hrs ] = +2%2F3+ jobs/hr
Krista's rate of working:
[ 1 job ] / [ t hrs ]
Their rate working together:
[ 8 jobs / 3 hrs ]
---------------------------
Add their rates of working:
+2%2F3+%2B+1%2Ft+=+8%2F3+
Multiply both sides by +3t+
+2t+%2B+3+=+8t+
+6t+=+3+
+t+=+1%2F2+
---------------
Krista takes 1/2 hr to do 1 job
-------------------------------
check answer:
+2%2F3+%2B+1%2Ft+=+8%2F3+
+2%2F3+%2B+1%2F%281%2F2%29+=+8%2F3+
+2%2F3+%2B+2+=+8%2F3+
+2%2F3+%2B+6%2F3+=+8%2F3+
+8%2F3+=+8%2F3+
OK

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
(2/3) + x = (8/3)
:
x = (8/3) - (2/3) = 2
:
****************************
krista does 2 jobs in 1 hour
****************************
:

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
There is a wide variety of similar solved joint-work problems with detailed explanations in this site. See the lessons
    - Using Fractions to solve word problems on joint work
    - Solving more complicated word problems on joint work
    - Selected joint-work word problems from the archive

Read them and get be trained in solving joint-work problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Rate of work and joint work problems" of the section "Word problems".