Question

Two students on bicycles leave their classroom building at 10:00 a.m. and travel in opposite directions. If the average speed of one of the students is 12 Km/h and the average speed of the other one is 14 km/h, at what time will they be 65 kilometers apart?

Answer 1

now... both are traveling in opposite direction
after some time "t", they cover altogether a distance of 65 miles
let's say, the one at 12mph cover a distance of "d",
thus
the other biker, cover the difference of that and 65, or 65-d
whatever "d" is

now, the time for both, is the exact same time,
since by the time they've covered 65 miles, let's say is
11:30am, is the same 11:30am for the first biker as well
as the second biker


`\bf \begin{array}{ccccllll} &distance&rate(mph)&time(hrs)\\\\ &-----&-----&-------\\\\ \textit{first biker}&d&12&t\\ \textit{second biker}&65-d&14&t \end{array}\\\\ -----------------------------\\\\ thus \\\\ \begin{cases} \boxed{d}=(12)(t) \\\\ 65-\boxed{d}=(14)(t) \end{cases}`

now... do you see the substitution there?
so.. do that, and solve for "t"