Question 796663
Philip's rate is ( 1 court ) / ( 45 min )
James's rate is ( 1 court ) / ( 30 min )
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What fraction of the court did they finish in 10 min ?
Let {{{ x }}} = that fraction
{{{ 1/45 + 1/30 = x/10 }}}
Multiply both sides by {{{ 90 }}}
{{{ 2 + 3 = 9x }}}
{{{ x = 5/9 }}}
5/9 of the court got mopped
That means 4/9 of the court was left
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Let {{{ t }}} = James time in minutes to mop 4/9 of the court
{{{ 1/30 = (4/9) / t }}}
{{{ 1/30 = 4 / (9t) }}}
Multiply both sides by {{{ 270t }}}
{{{ 9t = 4*30 }}}
{{{ 9t = 120 }}}
{{{ t = 13.333 }}} min
{{{ .333*60 = 20 }}}
It takes James 13 min and 20 sec to finish
check:
{{{ 1/30 = (4/9) / t }}}
{{{ 1/30 = .4444 / 13.333 }}}
{{{ 1/30 = 1/30 }}}
OK