Question

2 trains leave station 238 miles apart at same time toward each other. one at 80mph and other at 90mph. how long will it take for 2 trains to meet

Answer 1

`\bf \begin{array}{ccccllll} &distance&rate(mph)&time(hrs)\\\\ &-----&-----&-------\\\\ \textit{first train}&d&80&t\\ \textit{second train}&238-d&90&t \end{array}\\\\ -----------------------------\\\\ thus \\\\ \begin{cases} \boxed{d}=(80)(t)\\\\ 238-\boxed{d}=(90)(t) \end{cases}`

see the substitution? so.. do the substitution on the 2nd equation, and solve for "t"

bear in mind that, when the trains meet, over the same road, they have been traveling the same distance, one is faster than the other, so the distances differ, but the time does not, is the same for both,

if the first train has been running 45mins and met the second train,
then the second train has also been running for 45mins,
thus "t" is the same for both