Question 201785
Let {{{b}}} = speed of boat in still water
Let {{{c}}} = speed of current
Upstream:
Speed is {{{b - c}}}
{{{d[u] = (b - c)*t[u]}}}
Downstream:
speed is {{{b + c}}}
{{{d[d] = (b + c)*t[d]}}}
given:
{{{d[u] = 18}}}
{{{t[u] = 3}}}
{{{d[d] = 24}}}
{{{t[d] = 2}}}
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(1) {{{18 = (b - c)*3}}}
(2) {{{24 = (b + c)*2}}}
and
(1) {{{18 = 3b - 3c}}}
(2) {{{24 = 2b + 2c}}}
Multiply both sides of (1) by {{{2}}}
Multiply both sides of (2) by {{{3}}}
(1) {{{36 = 6b - 6c}}}
(2) {{{72 = 6b + 6c}}}
Add (1) and (2)
{{{108 = 12b}}}
{{{b = 9}}}
And, from (1),
{{{18 = 3*9 - 3c}}}
{{{3c = 27 - 18}}}
{{{3c = 9}}}
{{{c = 3}}}
The speed of the boat in still water is 9 mi/hr
The speed of the current is 3 mi/hr
check:
(1) {{{18 = (9 - 3)*3}}}
(2) {{{24 = (9 + 3)*2}}}
and
(1) {{{18 = 6*3}}}
{{{18 = 18}}}
(2) {{{24 = 12*2}}}
{{{24 = 24}}}
OK