Question 178714
Let the speed of her boat in still water = {{{s}}}
Let the speed of the current = {{{c}}}
Against the current:
{{{d[1] = r[1]*t[1]}}}
{{{r[1] = s - c}}}
{{{d[1] = (s - c)*t[1]}}}
with the current:
{{{d[2] = r[2]*t[2]}}}
{{{r[2] = s - c}}}
{{{d[2] = (s + c)*t[2]}}}
-------------------------
given:
{{{d[1] = 5}}} mi
{{{d[2] = 5}}} mi
{{{c = 4}}} mi/hr
{{{t[1] = t[2] + 20/60}}} hr (20 min is 20/60 of an hour)
--------------------------
Now I can write:
(1) {{{5 = (s - 4)*(t[2] + 1/3)}}}
(2) {{{5 = (s + 4)*t[2]}}}
I have 2 equations and 2 unknowns, so it should be solvable
Since both (1) and (2) = {{{5}}}, I'll set the right sides
equal to eachother
{{{(s - 4)*(t[2] + 1/3) = (s + 4)*t[2]}}}
Divide both sides by {{{t[2]}}}
{{{(s - 4)*(1 + (1/3)/t[2]) = s + 4}}}
{{{s - 4 + (s/3)/t[2] - (4/3)/t[2] = s + 4}}}
{{{(s/3 - 4/3)/t[2] = 8}}}
{{{s/3 - 4/3 = 8t[2]}}}
{{{s - 4 = 24t[2]}}}
{{{t[2] = (s - 4)/24}}}
Substitute this value of {{{t[2]}}} into (2)
(2) {{{5 = (s + 4)*t[2]}}}
(2) {{{5 = (s + 4)(s - 4)/24}}}
{{{s^2 - 16 = 120}}}
{{{s^2 = 136}}}
{{{s = 11.66}}}
Her boat will go 11.66 mi/hr in still water
check answer:
(2) {{{5 = (s + 4)*t[2]}}}
(2) {{{5 = (11.66 + 4)*t[2]}}}
{{{5 = 15.66t[2]}}}
{{{t[2] = 5/15.66}}}
{{{t[2] = .319}}}hrs
{{{t[1] = t[2] + 20/60}}}
{{{t[1] = .319 + .333}}}
{{{t[1] = .653}}}hrs
------------------------
(1) {{{5 = (s - 4)*(t[2] + 1/3)}}}
{{{5 = (11.66 - 4)*.653}}}
{{{5 = 7.66*.653}}}
{{{5 = 4.998}}} close enough
(2) {{{5 = (s + 4)*t[2]}}}
{{{5 = 15.66*.319}}}
{{{5 = 4.995}}} close enough
And, also {{{t[1]}}} should be 20 min
longer than {{{t[2]}}}
{{{t[1] - t[2] = .653 - .319}}}
{{{.653 - .319 = .334}}}
{{{.334*60 = 20.04}}}min close enough