Spacecraft I, containing students taking a physics exam, approaches the Earth with a speed of $0\mathrm{.}620$c $($relative to the Earth$),$ while spacecraft II$,$ containing professors proctoring the exam, moves at $0\mathrm{.}300$c $($relative to the Earth$)$ directly toward the students. The professors stop the exam after $80\mathrm{.}0$ min have passed on their clock.

$($a$)$

For what time interval $($in minutes$)$ does the exam last as measured by the students?

min

$($b$)$

For what time interval $($in minutes$)$ does the exam last as measured by an observer on Earth?

min