$($b$)$ A construction worker uses three types of hand$-$held vibratory tools in a working day $(8$ hours$).$ One has a vibration magnitude of $7\mathrm{.}2\frac{m}{s^2}$ and it is used for $80$ minutes. The second one has a vibration magnitude of $16\mathrm{.}8\frac{m}{s^2}$ and it is used for $20$ minutes. The last one has a vibration magnitude of $13\mathrm{.}8\frac{m}{s^2}.$ According to the guidance of the UK's Health and Safety Executive on handarm vibration exposure, what is the maximum allowable time $($in minutes$)$ of using the third one if the daily exposure limit value is not exceeded? Given:

$A(8)=2\mathrm{.}5\sqrt[\phantom{2}]{\frac{n}{100}}$ and $n=(\frac{a_{hv}}{2\mathrm{.}5}{)}^2\frac{t}{8}100$

where $A(8)=$ daily ibration exposure $(\frac{m}{s^2}),n=$ number of exposure points, $a_{hv}=$ vibration magnitude $(\frac{m}{s^2})$ and $t=$ daily exposure time $($hour$).$