Spacecraft I, containing students taking a physics exam, approaches the Earth with a speed of $0\mathrm{.}660$c $($relative to the Earth$),$ while spacecraft II$,$ containing professors proctoring the exam, moves at $0\mathrm{.}240$c$($relative to the Earth$)$ directly toward the students. The professors stop the exam after $44\mathrm{.}0$ 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

What If$?$ Suppose one of the professors proctored the exam by traveling on spacecraft I and stopped the exam after $44\mathrm{.}0$ min elapsed on her clock.

$($c$)$

For what time interval $($in minutes$)$ does the exam last as measured by the professors on spacecraft II$?$

min

$($d$)$

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

min