Question 923881
A man and a boy together can complete a work in 24 days.
let m = no. of days for the man to do the job alone
let b = no. of days for the boy to do it
let the completed job = 1
then a shared work equation
{{{24/m}}} + {{{24/b}}} = 1
 If for the last 6 days the man alone does the work, it is completed in 26 days.
The boy works only 20 days in this scenario
{{{26/m}}} + {{{20/b}}} = 1
Use elimination here,multiply the 1st equation by 5, the 2nd equation by 6
Subtract the 1st from the 2nd
{{{156/m}}} + {{{120/b}}} = 6
{{{120/m}}} + {{{120/b}}} = 5
------------------------------Subtraction eliminates b, find a
{{{36/m}}} = 1
m = 36 days the man working alone
:
then using the 1st original equation
{{{24/36}}} + {{{24/b}}} = 1
reduce the fraction
{{{2/3}}} + {{{24/b}}} = 1
{{{24/b}}} = 1 - {{{2/3}}}
{{{24/b}}} = {{{1/3}}}
Cross multiply
b = 72 days, the boy working alone
:
;
See if that checks out
{{{24/36}}} + {{{24/72}}} = 1
reduce fractions
{{{2/3}}} + {{{1/3}}} = 1
{{{24/36}}} + {{{24/b}}} = 1