need help with inverse problem

Question

anonymous · Answer

The amount of time it takes to build a road varies inversely with the number of workers building the road. Suppose it takes 40 workers 10 months to build the road. What is the constant of variation? Write an equation that could be used to determine how long it would take "n" workers to build the road.

ganeshie8 · Answer

The amount of time it takes to build a road varies inversely with the number of workers building the road.

ganeshie8 · Answer

say $n$ = number of workers
$t$ = time taken

$\large  t  \propto  \frac{1}{n}$

ganeshie8 · Answer

$\large   \implies$

$\large   t =  \frac{k}{n}$

ganeshie8 · Answer

Suppose it takes 40 workers 10 months to build the road.
                          n                t

anonymous · Answer

y = k/x
T = k/n where T is time and n is workers

Fill in the example it gives
10 = k/40

Solve for k
k = 400

Final equation
T = 400/n

ganeshie8 · Answer

substitute n, t values in above equation
and solve k

anonymous · Answer

thanks