Answer
$\Delta t'=10. s$
Work Step by Step
The dilated time is equal to $$\Delta t'=\gamma \Delta t_p$$ where $\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$. Substituting the known value of $v=0.84c$ yields a gamma value of $$\gamma=\frac{1}{\sqrt{1-0.84}}=2.5$$ Substituting values of $\Delta t_p=4.1s$ and $\gamma=2.5$ yields a dilated time of $$\Delta t'=(4.1s)(2.5)=10s$$
