Question 825961
Old machine's rate of working is:
( 1 unit of work ) / ( 12 hrs )
Rate of working with both machines:
( 1 unit of work ) / ( 4 hrs )
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Let the rate of the new machine be:
( 1 unit of work ) / ( t hrs )
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Add their rates of working to get their
rate of working together:
{{{ 1/12 + 1/t = 1/4 }}}
Multiply both sides by {{{ 12t }}}
{{{ t + 12 = 3t }}}
{{{ 2t = 12 }}}
{{{ t = 6 }}}
The new machine takes 6 hrs to do the work alone
check:
{{{ 1/12 + 1/t = 1/4 }}}
{{{ 1/12 + 1/6 = 1/4 }}}
{{{ 1/12 + 2/12 = 3/12 }}}
{{{ 3/12 = 3/12 }}}
OK