<PRE><B>Question 678128</B>
8 dug 3/8 of tunnel in 10 days.
 If they need to finish the remaining 5/8 of the tunnel in 7/3 days, how many more workers must they hire?
:
80 man-days to do 3/8 of the tunnel
:
let x = no. of man-days to do 5/8 of the tunnel
:
{{{80/x}}} = {{{(3/8)/(5/8)}}}
Cross multiply
{{{3/8}}}x = {{{5/8}}}*80
{{{3/8}}}x = 50
x = {{{8/3}}}*50
x = 133.33 man-days to do 5/8 of the tunnel
:
let w = additional workers needed to finish in 7/3 days
{{{7/3}}}(w+10) = 133.33
Multiply both sides by 3
7(w + 10) = 3(133.33)
7w + 70 = 400
7w = 400 - 70
7w = 330
w = 330/7
w ~ 47 additional men required
;
:
:
Check this:
{{{7/3}}}*57 = 133.33 man-days, the amt needed to do 5/8 of the job</PRE>