Question 977590
John's rate of cleaning:
[ 1 tank ] / [ 5 hrs ]
I will call Laura's rate of cleaning:
[ 1 tank ] / [ t hrs ]
Their rate of cleaning working together:
[ 1 tank ] / [ 3 hrs ]
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Add their rates of cleaning to get their
rate working together:
{{{ 1/5 + 1/t = 1/3 }}}
Multiply both sides by {{{ 15t }}}
{{{ 3t + 15 = 5t }}}
{{{ 2t = 15 }}}
{{{ t = 7.5 }}}
Working by herself, Laura takes 7 hrs and 30 min
to clean the tank
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check:
{{{ 1/5 + 1/t = 1/3 }}}
{{{ 1/5 + 1/7.5 = 1/3 }}}
{{{ 1/5 + 2/15 = 1/3 }}}
{{{ 3/15 + 2/15 = 5/15 }}}
{{{ 5/15 = 5/15 }}}
OK