Question 734376
Let {{{ t }}} = time in hours for new sweeper to clean street
The new sweeper's rate of sweeping is ( 1 street cleaned ) / ( t hrs )
The old sweeper's rate of sweeping is ( 1 street cleaned / 30 hrs )
Together, their rate is ( 1 street cleaned ) / ( 7.5 hrs )
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Add their rates of sweeping to get their rate sweeping together
{{{ 1 / 30 + 1 / t = 1/ 7.5 }}}
Multiply both sides by {{{ 30t }}}
{{{ t + 30 = 4t }}}
{{{ 3t = 30 }}}
{{{ t = 10 }}}
It will take the new sweeper 10 hrs to clean street
check:
{{{ 1/30 + 3/30 = 4/30 }}}
{{{ 4/30 = 4/30 }}}
OK