Question 686684
You rightly concluded that the boat goes upstream at {{{(8-r)}}} mph
and downstream at {{{(8+r)}}} mph.
The time needed to travel {{{30}}} miles downstream is {{{30/(8+r)}}}
The time to travel {{{36}}} miles upstream is {{{36/(8-r)}}},
which is twice as long a time, so
{{{highlight(36/(8-r)=2*(30/(8+r)))}}}
Now that we have our equation, we solve it
{{{36/(8-r)=2*(30/(8+r))}}} --> {{{36/(8-r)=60/(8+r)}}} to simplify it a bit.
Form there, we "equate the cross-products",
which is the same as multiplying both sides times {{{(8-r)(8+r)}}}
{{{36/(8-r)=60/(8+r)}}} --> {{{36(8+r)=60(8-r)}}} --> {{{36*8+36r=60*8-60r}}} --> {{{288+36r=480-60r}}}
{{{288+36r=480-60r}}} --> {{{288+36r+60r-288=480-60r+60r-288}}} --> {{{36r+60r=480-288}}} --> {{{96r=192}}} --> {{{96r/96=192/96}}} --> {{{highlight(r=2)}}}