Question 1080277
1st custodian's rate of working:
[ 1 office cleaned ] / [ 2 hrs ]
Their rate working together:
[ 1 office cleaned ] / [ 4/3 hrs ]
Let {{{ t }}} = the second worker's time
in hrs to clean the office
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Add their rates of working to get their
rate working together
{{{ 1/2 + 1/t = 1/((4/3)) }}}
{{{ 1/2 + 1/t = 3/4 }}}
Multiply both sides by {{{ 4t }}}
{{{ 2t + 4 = 3t }}}
{{{ t = 4 }}}
The 2nd worker takes 4 hrs to do the job alone
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check:
{{{ 1/2 + 1/t = 3/4 }}}
{{{ 1/2 + 1/4 = 3/4 }}}
{{{ 2/4 + 1/4 = 3/4 }}}
{{{ 3/4 = 3/4 }}}
OK