SOLUTION: how do you solve problems that are combining two peoples progress for example johnny wash 20 dishes in 2 hours .Sarah washed 20 dishes in 1.5 hours. how long will it take for them

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Question 461030: how do you solve problems that are combining two peoples progress for example johnny wash 20 dishes in 2 hours .Sarah washed 20 dishes in 1.5 hours. how long will it take for them to wash 20 dishes together....how are these problems solved and what type of problems are these
Found 2 solutions by ankor@dixie-net.com, rwm:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
johnny wash 20 dishes in 2 hours .Sarah washed 20 dishes in 1.5 hours.
how long will it take for them to wash 20 dishes together.
:
Let t = time required when they work together
:
Let the completed job = 1 (20 clean dishes)
:
This is a shared work problem
Each does a fraction of the job, the two fractions add up to 1
:
+ = 1
Multiply by 6
6* + 6* = 6(1)
cancel the denominators
3t + 4t = 6
7t = 6
t = hrs working together, that's about *60 = 51.4 min
:
:
Check this, = .857 hrs
.857/2 + .857/1.5 =
.43 + .571 = 1.00 confirms our solution

Answer by rwm(914) (Show Source):
You can put this solution on YOUR website!
This is known as a work problem.
johnny wash 20 dishes in 2 hours .
Sarah washed 20 dishes in 1.5 hours.
how long will it take for them to wash 20 dishes together....how are these problems solved and what type of problems are these
since each part talks about 20 dishes we will call it "one" job.
in one hour john does 1/2 of the job
in one hour sarah does 1/1.5 or 2/3 of the job
x/2+x/1.5=1
x/2+2x/3=1
multiply by 6
3x+4x=6
7x=6
x=6/7 of one hour to do one job
check
6/7/2+6/7/1.5=1
3/7+4/7=1
ok