Question

Two truck drivers leave a cafe at the same time, traveling in opposite directions. One truck goes 1 mph faster than the other one. After 3 hr, they are 291 miles apart. How fast is each truck going?

Answer 1

so hmmm notice, let's say two, trucks, truck A and truck B,
so truck B is going faster by 1mph than truck A

notice, the distance between them is 291 after 3hrs,
that means, both truck drivers, have been driving for 3hrs,
and covered both combined 291,
let us say, A covered distance "d", so, B covered the rest of it,
or 291 - d,
though their distance and rate differs some, their driving time is
the same 3hrs though
thus
`\bf \begin{array}{ccccllll} &distance&rate&time(hrs)\\ &\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\ A&d&r&3\\ B&291-d&r+1&3 \end{array} \\\\ \begin{cases} d=(r)(3)\to d=\boxed{3r} \\\\ 291-d=(r+1)(3)\\ --------------\\ 291-\boxed{3r}=(r+1)(3) \end{cases}`

solve for "r", that's how fast truck A was going

what about truck B? well, B was going r + 1