Question 732453
Beteena can clear the snow in five hrs.
In 2 hrs, working alone, she can clear
{{{ 2/5 }}} of the driveway.
That means {{{ 3/5 }}} is left to clear.
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Add their rates of working to get rate
working together.
( 1 driveway / 4 hrs ) + ( 1 driveway / 5 hrs ) = ( 3/5 d.w. / t hrs )
{{{ 1/4 + 1/5 = (3/5) / t }}}
{{{ 1/4 + 1/5 = 3 / (5t) }}}
Multiply both sides by {{{ 20t }}}
{{{ 5t + 4t = 12 }}}
{{{ 9t = 12 }}}
{{{ t = 4/3 }}}
1 hr plus 1/3 of an hr is
1 hr and 20 min
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check:
{{{ 1/4 + 1/5 = (3/5) / t }}}
{{{ 1/4 + 1/5 = (3/5) / (4/3) }}}
{{{ 5/20 + 4/20 = (3/5)*(3/4) }}}
{{{ 9/20 = 9/20 }}}
OK