Question 236019
Write a separate equation for each
part of the trip
upstream:
{{{d[1] = r[1]*t[1]}}}
(1) {{{d[1] = 5*t[1]}}} mi
downstream:
{{{d[2] = r[2]*t[2]}}}
(2) {{{d[2] = 11*t[2]}}} mi
also:
{{{d[1] = d[2]}}} (I'll call them both {{{d}}})
{{{t[1] + t[2] = 4}}} hrs
{{{t[2] = 4 - t[1]}}} hrs
--------------------------
(1) {{{d = 5t[1]}}}
(2) {{{d = 11*(4 - t[1])}}}
(2) {{{d = 44 - 11t[1]}}}
Subtract (1) from (2)
{{{0 = 44 - 11t[1] - 5t[1]}}}
{{{11t[1] + 5t[1] = 44}}}
{{{16t[1] = 44}}}
{{{t[1] = 2.75}}} hrs
and, since
{{{t[2] = 4 - t[1]}}}
{{{t[2] = 4 - 2.75}}}
{{{t[2] = 1.25}}}
-----------------------
(1) {{{d[1] = 5*t[1]}}}
{{{d[1] = 5*2.75}}}
{{{d[1] = 13.75}}} mi
and
{{{d[2] = 11*t[2]}}}
{{{d[2] = 11*1.25}}}
{{{d[2] = 13.75}}} mi
Both distances are the same, as they should be
Mark rowed {{{13.75 + 13.75 = 27.5}}} mi