Question 267333
The equation for paddling against the current is:
{{{d[1] = (s - c)*t[1]}}}
The equation for paddling with the current is:
{{{d[2] = (s + c)*t[2]}}}
where
{{{s}}} = speed paddling in still water
{{{c}}} = speed of the current
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given:
{{{d[1] = 20}}} km
{{{d[2] = 20}}} km
{{{t[1] = 6}}} hrs
{{{t[2] = 5}}} hrs
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Plugging in numbers:
(1) {{{20 = (s - c)*6}}}
and
(2) {{{20 = (s + c)*5}}}
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(1) {{{20 = 6s - 6c}}}
(2) {{{20 = 5s + 5c}}}
I'll multiply both sides of (2) by {{{6/5}}}
(2) {{{(6/5)*20 = 6s + 6c}}}
(2) {{{24 = 6s + 6c}}}
Now add (1) and (2)
(2) {{{24 = 6s + 6c}}}
(1) {{{20 = 6s - 6c}}}
{{{44 = 12s}}}
{{{s = 11/3}}} km/hr
From (2):
{{{4 = s + c}}}
{{{4 = 11/3 + c}}}
{{{c = 12/3 - 11/3}}}
{{{c = 1/3}}} km/hr
In still water, they can paddle 11/3 km/hr
The speed of the current is 1/3 km/hr
check:
(1) {{{20 = (s - c)*6}}}
(1) {{{20 = (10/3)*6}}}
(1) {{{20 = 20}}}
and
(2) {{{20 = (s + c)*5}}}
(2) {{{20 = (12/3)*5}}}
(2) {{{20 = 20}}}
OK