I am doing a school assignment to calculate the number of employees required to complete a construction contract.
$3$ workers take $1.5$ hours to complete $5000$ units of work. If there are $437,400$ units of work, and only $128$ hours to complete it, how many employees will you need?
Update
Ok I had a go at solving this using the rule of three.
it takes 3 workers 1.5 hours to create 5K
it takes X workers 128 hours to create 437.4k
5K/1.5/3 = 437.4K/128/X
=> X = (437.4K * 1.5 * 3)/(5K*128)
=> 3
Was this the correct solution?
$3$ workers taking $1.5$ hours (so $4.5$ worker-hours) to complete $5000$ units of work means $\frac{5000}{4.5} \approx 1111.1111$ units of work per worker hour.
$437,400$ units of work would then take about $\frac{437400}{1111.1111}\approx 393.66$ worker-hours, i.e. about $\frac{393.66}{128}\approx 3.075$ workers in $128$ hours.
You have rounded this to $3$. But that is not exactly correct: $3$ workers would do about $426,666.67$ units of work in $128$ hours, which is not quite enough; a $4$th work needs to do $9.66$ hours work to make up the difference.