Question 509721
Let {{{s}}} = speed of boat in still water
Let {{{t}}} = time it takes to go either upstream or downstream
{{{ c = 4 }}} is the speed of the current
{{{ s + c }}} is the boat's speed going downstream
{{{ s - c }}} is the boat's speed going upstream
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given:
Going upstream:
(1) {{{ 48 = (s - 4)*t }}}
Going downstream:
(2) {{{ 72 = (s + 4)*t }}}
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(1) {{{ 48 = s*t - 4t }}}
and
(2) {{{ 72 = s*t + 4t }}}
Subtract (1) from (2)
(2) {{{ 72 = s*t + 4t }}}
(1) {{{ -48 = -s*t + 4t }}}
{{{ 24 = 8t }}}
{{{ t = 3 }}}
By substitution:
(1) {{{ 48 = (s - 4)*3 }}}
(1) {{{ 48 = 3s - 12 }}}
(1) {{{ 3s = 60 }}}
(1) {{{ s = 20 }}}
The speed in still water is 20 mi/hr
check answer:
(2) {{{ 72 = (20 + 4)*3 }}}
(2) {{{ 72 = 24*3 }}}
(2) {{{ 72 = 72 }}}
OK