Question 461030
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.
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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
:
{{{t/2}}} + {{{t/1.5}}} = 1
Multiply by 6
6*{{{t/2}}} + 6*{{{t/1.5}}} = 6(1)
cancel the denominators
3t + 4t = 6
7t = 6
t = {{{6/7}}} hrs working together, that's about {{{6/7}}}*60 = 51.4 min
:
:
Check this, {{{6/7}}} = .857 hrs
.857/2 + .857/1.5 = 
.43 + .571 = 1.00 confirms our solution