\magnification=\magstep2

$$
{\rm E_A} \quad = \quad 5 {\rm\ GeV}  \quad = \quad 8 \times 10^{10} {\rm\ J}
$$

$$
{\rm E_A} \quad = \quad  \gamma_A {m_p} c^2 
$$

$$
\gamma_A = 5.33
$$

$$
v_A \quad = \quad 0.982242 c  \quad = \quad 2.94469 \times 10^8 {\rm m/s}
$$

$$
\eqalign{
  t_A \quad &= \quad { {1.5 \times 10^{11} {\rm\ m}} 
                  \over {2.94469 \times 10^{8} {\rm \ m/s}}} \cr
            &\phantom{=} \cr
            &= \quad 509.4 {\rm \ seconds} \cr
}
$$


$$
{\rm E_B} \quad = \quad 10 {\rm\ GeV}  \quad = \quad 16 \times 10^{10} {\rm\ J}
$$

$$
{\rm E_B} \quad = \quad  \gamma_B {m_p} c^2 
$$

$$
{\gamma}_B = 10.66
$$

$$
v_B \quad = \quad 0.995590 c  \quad = \quad 2.98470 \times 10^8 {\rm m/s}
$$

$$
\eqalign{
  t_B \quad &= \quad { {1.5 \times 10^{11} {\rm\ m}} 
                  \over {2.98470 \times 10^{8} {\rm \ m/s}}} \cr
            &\phantom{=} \cr
            &= \quad 502.6 {\rm \ seconds} \cr
}
$$


$$
t_A - t_B \quad = \quad 6.8 {\rm \ seconds }
$$

\bye

