Question 494483
George and Stanley are builfing a stone fence.
 They can complete the fence together in 11hrs. George can complete it in 33 hrs working alone.
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Let s = Stanley's working time alone
let the completed job = 1
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A shared work equation to find Stanley's working time alone
{{{11/33}}} + {{{11/s}}} = 1
multiply by 33s, results:
11s + 33(11) = 33s
363 = 33s - 11s
363 = 22s
s = {{{363/22}}}
s = 16.5 hrs is Stanley's working time alone
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If they work together for 6 hours, then Stanley goes to the pub for a pint, How much longer must George work to finish the fence?
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let g = length of time George works after Stanley leaves
then
(g + 6) = Georges total working time
A shared work equation for this scenario
{{{((g+6))/33}}} + {{{6/16.5}}} = 1
Multiply by 544.5 (33*16.5), to clear the denominators, results
16.5(g+6) + 33(6) = 544.5
16.5g + 99 + 198 = 544.5
16.5g + 297 = 544.5
16.5g = 544.5 - 297
16.5g = 247.5
g = {{{247.5/16.5}}}
g = 15 more hrs for thirsty George
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