Question 749509
Rate of resurfacing for new machine:
( 1 mile ) / ( 10 hrs )
Rate for older machine:
( 1 mile ) / ( 18 hrs )
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Let {{{ t }}} = the time in hours for them to
resurface 1 mile working together
{{{ 1/10 + 1/18 = 1/t }}}
Multiply both sides by {{{ 90t }}}
{{{ 9t + 5t = 90 }}}
{{{ 14t = 90 }}}
{{{ t = 6.429 }}}
{{{ .429*60 = 25.7 }}}
It will take them 6 hrs and 26 min working together
check:
{{{ 1/10 + 1/18 = 1/t }}}
{{{ 1/10 + 1/18 = 1/6.429 }}} 
{{{ .1 + .05556 = .15555 }}}
{{{ .1555 = .1555 }}}
OK
For 20 miles:
{{{ 1/10 + 1/18 = 20/t[2] }}}
{{{ 9t + 5t = 20*90 }}}
{{{ 14t = 1800 }}}
{{{ t = 128.571 }}}
{{{ .571*60 = 34.3 }}}
It will take them 128 hrs and 34 min
check:
{{{ 1/10 + 1/18 = 20/t[2] }}}
{{{ 1/10 + 1/18 = 20/128.571 }}}
{{{ .1 + .05556 = .15556 }}}
{{{ .15556 = .15556 }}}
OK