Question 342305
You need 2 equations: 1 for upstream and 1 for downstream
{{{d[u] = r[u]* t[u]}}}
{{{d[d] = r[d]* t[d]}}}
Let rate of current = {{{r[c]}}}
Let rate in still water = {{{r[s]}}}
{{{r[u] = r[s] - r[c]}}} mi/hr
{{{r[d] = r[s] + r[c]}}} mi/hr
given:
{{{d[u] = 30}}} mi
{{{d[d]] = 30}}} mi
{{{r[c] = 5}}} mi/hr
{{{t[d] = t[u] - 1}}} hr
{{{r[u] = r[s] - 5}}} mi/hr
{{{r[d] = r[s] + 5}}} mi/hr
-----------------
{{{d[u] = r[u]* t[u]}}}
{{{30 = (r[s] - 5)*t[u]}}}
{{{t[u] = 30/(r[s] - 5)}}}
and
{{{d[d] = r[d]* t[d]}}}
{{{30 = (r[s] + 5)* (t[u] - 1)}}}
{{{30 = r[s]*t[u] + 5t[u] - r[s] - 5}}}
By substitution:
{{{30 = r[s]*(30/(r[s] - 5)) + 5*(30/(r[s] - 5)) - r[s] - 5}}}
Multiply both sides by {{{r[s] - 5}}}
{{{30*(r[s] - 5) = 30r[s] + 150 - (r[s] + 5)*(r[s] - 5)}}}
{{{30r[s] - 150 = 30r[s] + 150 - (r[s])^2 - 25}}}
{{{(r[s])^2  = 275}}}
{{{r[s] = 16.58}}} mi/hr
check answer:
{{{30 = (r[s] - 5)*t[u]}}}
{{{30 = (16.58 - 5)*t[u]}}}
{{{30 = 11.58*t[u]}}}
{{{t[u] = 2.59}}} hrs
{{{t[d] = 1.59}}} hrs
{{{r[u] = r[s] - 5}}}
{{{r[u] = 16.58 - 5}}}
{{{r[u] = 11.58}}}
{{{r[d] = 16.58 + 5}}}
{{{r[d] = 21.58}}}
{{{d[d] = r[d]* t[d]}}}
{{{30 = 21.58*1.59}}}
{{{30 = 34.31}}} this is wrong
{{{d[u] = r[u]* t[u]}}}
{{{30 = 11.58*2.59}}}
{{{30 = 29.99}}} OK
Something went wrong somewhere- answer doesn't 
quite check. My method is good, though.
See if you can find error