Question 833242
Call painting the 200 ft2 fence 1 job
{{{ 1/40 }}} = 1 job/40 min
Then a 500 ft2 fence would be 2.5 jobs
Let {{{ R }}} = Tom's rate of painting
{{{ 4R }}} = Huck's rate of painting
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{{{ R + 4R = 1/40 }}}
{{{ 5R = 1/40 }}}
{{{ R = 1/200 }}}
{{{ 4R = 1/50 }}}
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For Tom:
{{{ R = 2.5/t }}}
{{{ 1/200 = 2.5/t }}}
{{{ t = 2.5*200 }}}
{{{ t = 500 }}}
For Huck:
{{{ 4R = 2.5/t }}}
{{{ 1/50 = 2.5/t }}}
{{{ t = 2.5*50 }}}
{{{ t = 125 }}}
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{{{ 500/60 = 8 + 20/60 }}}
Tom takes 8 hrs and 20 min to paint the 500 ft2 fence alone
{{{ 125/60 = 2 + 5/60 }}}
Huck takes 2 hrs and 5 min to paint the 500 ft2 fence alone
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check:
{{{ R + 4R = 1/40 }}}
{{{ 1/200 + 1/50 = 1/40 }}}
{{{ 1/200 + 4/200 = 1/40 }}}
{{{ 5/200  = 1/40 }}}
{{{ 1/40 = 1/40 }}}
OK