Question

 The distance between city A and B is 600 km. The first train left A and headed towards B at the speed of 60 km/hour. The second train left B heading towards A three hours after the first train left A, and it traveled with a speed of v km/hour. The trains met t hours after the time at which the first train left A. Express v in terms of t. Find the speed v if t=7; t=6.

Answer 1

`\bf \begin{array}{ccccllll} &distance&rate(km/hr)&time(hrs)\\ &\textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\\ A&d&60&t\\ B&600-d&v&t+3 \end{array}`


`\bf \textit{meaning}\implies \begin{cases} d=(60)(t) \\ \quad \\ 600-d=(v)(t+3)\\ ------------\\ d=\boxed{60t}\qquad thus \\ \quad \\ 600-\boxed{60t}=v(t+3)\leftarrow \textit{solve for`

keep in mind, that "t" is the time when the train at A station, left towards B station

they met, at some time "t", and by the time that happened, train from A
which started 3 hours earlier, had already covered "d" distance,
whatever that is
and the train coming from B, covered, 600-d, or the difference