Question 496656
In work problems, you add their rates of
working to get their rate working together.
A's rate is ( 1 job ) / ( 10 days ) = {{{ 1/10 }}}
B's rate is ( 1 job ) / ( x days ) = {{{ 1/x }}}
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The question to ask is: " What part of the job
does A get done in 2 days?"
If he does 1 job in 10 days, he does 1/10
of a job in 1 day. That means he does 2/10
or 1/5 of a job in 2 days.
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So, there is {{{ 1 - 1/5 = 4/5 }}} of the job left
to do when B joins him
So, they do 4/5 of the job together in 3 days
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Adding their rates of working:
{{{ 1/10 + 1/x = (4/5)/3 }}}
{{{ 1/10 + 1/x = 4/15 }}}
Multiply both sides by {{{ 30x }}}
{{{ 3x + 30 = 8x }}}
{{{ 5x = 30 }}}
{{{ x = 6 }}}
B alone could have done the work in 6 hours