Question 841655
The brick layer builds ( 1 wall ) / ( 6 hrs )
That's the same as ( 1/6 wall ) / ( 1 hour )
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The apprentice builds ( 1 wall ) / ( 16 hrs )
That's the same as ( 1/16 wall ) / ( 1 hour )
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Let {{{ t }}} = the time that the brick layer works
{{{ t + 5 }}} = the timer the apprentice works
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( brick layer's rate ) x ( brick layer's time ) +
( apprentice's rate ) x ( apprentice's time ) = 1
( 1 is the whole job )
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{{{ ( 1/6 )*t + ( 1/16 )*( t + 5 ) = 1 }}}
Multiply both sides by {{{ 48 }}}
{{{ 8t + 3t + 15 = 48 }}}
{{{ 11t = 33 }}}
{{{ t = 3 }}}
{{{ t + 5 = 8 }}}
the brick layer works 3 hrs
The apprentice works 8 hrs
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check:
{{{ ( 1/6 )*t + ( 1/16 )*( t + 5 ) = 1 }}}
{{{ ( 1/6 )*3 + ( 1/16 )*( 3 + 5 ) = 1 }}}
{{{ 1/2 + 1/2 = 1 }}}
OK