<PRE><B>Question 994811</B>
 Paul and Derick complete a certain job if Paul works for 3 days and Derick works for 2 days or if they both work for 2 2/5 days.
 How long will it take each to do the job alone?
:
let p = time required if Paul works alone
let d = time required if Derick works alone
let the completed job = 1
:
Write an equation for each scenario
:
{{{3/p}}} + {{{2/d}}} = 1 
and change 2{{{2/5}}} days to 2.4 days
{{{2.4/p}}} + {{{2.4/d}}} = 1 
:
we can use elimination here, multiply the 1st equation by 8, the 2nd equation by 10.
{{{24/p}}} + {{{16/d}}} = 8
{{{24/p}}} + {{{24/d}}} = 10
-----------------------------Subtract the 1st eq from the 2nd and you have 
{{{8/d}}} = 2
8 = 2d
d = 4 days for Derick working alone
:
Use the first equation to find p
{{{3/p}}} + {{{2/4}}} = 1 
{{{3/p}}} = 1 - {{{1/2}}} 
{{{3/p}}} = {{{1/2}}} 
p = 3*2
p = 6 days for Paul alone
:
:
Confirm this in the 2nd equation
{{{2.4/6}}} + {{{2.4/4}}} = 1 
.4 + .6  = 1</PRE>