Answer
$16$ hours.
Work Step by Step
Step 1:- Translate the statement to form an equation.
Let the time required be $T$,
the number of computers be $N$,
and the number of workers be $W$.
Because $T$ varies directly as $N$ and inversely as $W$, we have
$\Rightarrow T=\frac{kN}{W}$ ...... (1)
Step 2:- Substitute the first set of values into the equation to find the value of $k$.
The given values are $N=30$ computers ,$W=6$ workers and $T=10$ hours.
Substitute into the equation (1).
$\Rightarrow 10=\frac{k(30)}{6}$
Simplify.
$\Rightarrow 10=5k$
Divide both sides by $5$.
$\Rightarrow \frac{10}{5}=\frac{5k}{5}$
Simplify.
$\Rightarrow 2=k$
Step 3:- Substitute the value of $k$ into the original equation.
Substitute $k=2$ into the equation (1).
$\Rightarrow T=\frac{2N}{W}$ ...... (2)
Step 4:- Solve the equation to find the required value.
Substitute $W=5$ workers and $N=40$ computers into the equation (2).
$\Rightarrow T=\frac{2(40)}{5}$
Simplify.
$\Rightarrow T=16$
Hence, the time required is $16$ hours.
