Question 270602
Let {{{s}}} = speed of stream in km/hr
Let {{{b}}} = speed of boat in still water in km/hr
Upstream:
{{{d[1] = (b - s)*t[1]}}}
Downstream:
{{{d[2] = (b + s)*t[2]}}}
given:
{{{s = 3}}} km/hr
{{{d[1] = 4}}} km
{{{d[2] = 10}}} km
{{{t[1] = t[2]}}} (I'll just call it {{{t}}})
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(1) {{{4 = (b - 3)*t}}}
(1) {{{t = 4/(b - 3)}}}
and
(2) {{{10 = (b + 3)*t}}}
(2) {{{t = 10/(b + 3)}}}
Since {{{t}}} is the same in both,
{{{4/(b - 3) = 10/(b + 3)}}}
Multiply both sides by {{{(b-3)*(b+3)}}}
{{{4*(b + 3) = 10*(b - 3)}}}
{{{4b + 12 = 10b - 30}}}
{{{6b = 42}}}
{{{b = 7}}}
The speed of the boat on still water is 7 km/hr
check:
(1) {{{4 = (b - 3)*t}}}
(1) {{{4 = (7 - 3)*t}}}
(1) {{{4 = 4t}}}
{{{t = 1}}} hr
and
(2) {{{10 = (b + 3)*t}}}
(2) {{{10 = (7 + 3)*t}}}
(2) {{{10 = 10t}}}
{{{t = 1}}} hr
OK