$(3$ marks: $1\mathrm{.}5,1,0\mathrm{.}5)$

$($i$)$ One person using a hammer will take $5$ days to nail new shingles on the roof of a $300m^2$ house.

$($ii$)$ Two persons using a hammer but working together $($one holds a shingle, the other swings the hammer$)$ will take $2$ days to do the same job.

$($iii$)$ One person using a nail gun will take $1$ day to do the same job.

a$.$ Calculate the labour productivity $($in $m^2$ per worker per day$)$ for each of the above cases.