Question 162663
Let his rate in still water = {{{s}}}
Let the rate of the current = {{{c}}}
His rate against the current is {{{s - c}}}
His rate with the current is {{{s + c}}}
The distance both ways is {{{10}}}km
distance = rate * time
(1) {{{10 = (s + c)*5}}} mi (with the current)
(2) {{{10 = (s - c)*21.5}}} mi (against the current)
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(1) {{{10 = 5s + 5c}}}
(2) {{{10 = 21.5s - 21.5c}}}
Multiply both sides of (2) by {{{10}}}
(2) {{{100 = 215s - 215c}}}
Multiply both sides of (1) by {{{43}}}
(1) {{{430 = 215s + 215c}}}
(2) {{{100 = 215s - 215c}}} Now add the equations
(3) {{{530 = 430s}}}
{{{s = 1.233}}}km/hr
(1) {{{10 = 5s + 5c}}}
{{{5c = 10 - 5*1.233}}}
{{{5c = 10 - 6.163}}}
{{{5c = 3.837}}}
{{{c = .7674}}}km/hr
His rate in still water is 1.233 km/hr
The rate of the current is .7674 km/hr
check answer:
(1) {{{10 = (s + c)*5}}} 
(2) {{{10 = (s - c)*21.5}}}
--------------------------
(1) {{{10 = (1.233 + .7674)*5}}}
{{{10 = 2.0004*5}}}
{{{10 = 10.002}}} error due to rounding off
(2) {{{10 = (s - c)*21.5}}}
{{{10 = (1.233 - .7674)*21.5}}}
{{{10 = .4656*21.5}}}
{{{10 = 10.010}}} (error due to rounding)
OK