Find the value of each of the following:

$125\%$ of $4$ hours $40$ minutes.

Step 1: Convert $4$ hours $40$ minutes into hours.

Given: $125\%$ of $4$ hours $40$ minutes.

We know that

$60$ minutes $=1$hour.

$\Rightarrow 1$minute $=\frac{1}{60}$hour.

$\Rightarrow 40$minute $=\frac{40}{60}$hour.

$\Rightarrow 40$minute $=\frac{2}{3}$hour.

Thus, $4$ hours $40$ minutes $=4$ hours $+40$ minutes

$=4$hours $+\frac{2}{3}$hours

$$\begin{gathered} =4+\frac{2}{3} \\ =\frac{12+2}{3} \\ =\frac{14}{3}\mathrm{hours} \end{gathered}$$

Hence, $4$ hours $40$ minutes $=\frac{14}{3}$hours.

Step 2: Find $125\%$ of $4$ hours $40$ minutes.

Since, $\%=\frac{1}{100}$.

Now,

$125\%$ of $4$ hours $40$ minutes$=125\%$ of $\frac{14}{3}$ hours.

$$\begin{gathered} =\frac{14}{3}\times 125\% \\ =\frac{14}{3}\times \frac{125}{100} \\ =\frac{14}{3}\times \frac{5}{4} \\ =\frac{70}{12} \\ =\frac{35}{6} \end{gathered}$$

Hence, $125\%$ of $4$ hours $40$ minutes $=\frac{35}{6}$hours $=5\frac{5}{6}$hours.