Question 319437
Let {{{c}}} = speed of current
{{{15 - c}}} = speed going upstream
{{{15 + c}}} = speed going downstream
(1){{{36 = (15 - c)*t[u]}}}
(2) {{{36 = (15 + c)*t[d]}}}
(3) {{{t[u] + t[d] = 5}}}
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(1){{{36 = (15 - c)*t[u]}}}
{{{t[u] = 36/(15 - c)}}}
and
(2) {{{36 = (15 + c)*t[d]}}}
{{{t[d] = 36/(15 + c)}}}
Adding:
{{{t[u] + t[d] = 36*(1/(15 - c) + 1/(15 + c))}}}
{{{5 = 36*(1/(15 - c) + 1/(15 + c))}}}
Multiply both sides by {{{(15 - c)(15 + c)}}}
{{{5*(225 - c^2) = 36*(15 + c + 15 - c)}}}
{{{1125 - 5c^2 = 36*30}}}
{{{5c^2 = 1125 - 1080}}}
{{{5c^2 = 45}}}
{{{c^2 = 9}}}
{{{c = 3}}}
The current is 3 mi/hr
check:
{{{t[u] + t[d] = 36*(1/(15 - c) + 1/(15 + c))}}}
{{{t[u] + t[d] = 36*(1/(15 - 3) + 1/(15 + 3))}}}
{{{t[u] + t[d] = 36*(1/12 + 1/18)}}}
{{{t[u] + t[d] = 36/12 + 36/18}}}
{{{t[u] + t[d] = 3 + 2}}}
OK