Question 746799
peter and Paul can do a certain job in 3 hours.
let x = Pete's time working alone
let y = Paul's time
let the completed job = 1
:
A shared work equation
{{{3/x}}} + {{{3/y}}} = 1
:
on a given day, they worked together for 1 hour then Paul left and peter finishes the rest of the work in 8 more hours?
Then Pete works 9 hrs.
{{{9/x}}} + {{{1/y}}} = 1
:
We can use elimination here, multiply above equation by 3
Subtract the 1st equation
{{{27/x}}} + {{{3/y}}} = 3
{{{3/x}}} + {{{3/y}}} = 1
--------------Subtraction eliminates y, find x
{{{24/x}}} = 2
2x = 24
x = 12 hrs for Peter to do the job alone?
:
:
See if that checks out, find y:
{{{3/12}}} + {{{3/y}}} = 1
{{{1/4}}} + {{{3/y}}} = 1
y = 4
Check in the 2nd equation
{{{9/12}}} + {{{1/4}}} = 1; confirms our solutions of x = 12 & y = 4