Question 208993
Eva can wallpaper a room in 4 hours and Kathy can wallpaper the same room in 6 hours. 
Kathy works on her own for one hour, and is then joined bye Eva.
 Assuming these rates, how many hours did Kathy and Eva together take to finish the job?
:
Let t = time required when they work together
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Let the completed job = 1
:
Each will do a fraction of the job. the two fractions add up to 1
{{{t/4}}} + {{{t/6}}} = 1
Multiply equation by 12
12*{{{t/4}}} + 12*{{{t/6}}} = 12*1
Cancel denominators
3t + 2t = 12
:
5t = 12
t = {{{12/5}}}
t = 2.4 hrs working together
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Check solution:
{{{2.4/4}}} + {{{2.4/6}}} = 
.6 + .4 = 1