Question 190239
For Joe:
(1) {{{d[j] = r[j]*t[j]}}}
For Ron:
(2) {{{d[r] = r[r]*t[r]}}}
given:
{{{r[j] = 8}}} mi/hr
{{{r[r] = 4}}} mi/hr
{{{d[j] + d[r] = 44}}} mi
{{{t[j] = t[r] + 1/4}}} hr
----------------------
(1) {{{d[j] = 8t[j]}}}
(2) {{{d[r] = 4t[r]}}}
and
{{{d[j] + d[r] = 44}}}
{{{d[j] = 44 - d[r]}}}
therefore
(1) {{{44 - d[r] = 8t[j]}}}
(2) {{{d[r] = 4t[r]}}}
also
{{{t[j] = t[r] + 1/4}}}
therefore
(1) {{{44 - d[r] = 8*(t[r] + 1/4)}}}
(2) {{{d[r] = 4t[r]}}}
-------------------------
(1) {{{44 - d[r] = 8t[r] + 2}}}
(1) {{{8t[r] + d[r] = 42}}}
and
(2) {{{4t[r] - d[r] = 0}}}
Add (1) and (2)
{{{12t[r] = 42}}}
{{{t[r] = 3.5}}}
and, since
(2) {{{d[r] = 4t[r]}}}
{{{d[r] = 4*3.5}}}
{{{d[r] = 14}}} mi
and also
{{{d[j] + d[r] = 44}}}
{{{d[j] + 14 = 44}}}
{{{d[j] = 30}}} mi
Ron went 14 mi and Joe went 30 mi
check answer:
{{{t[j] = t[r] + 1/4}}}
{{{t[j] = 3.5 + .25}}}
{{{t[j] = 3.75}}}
(1) {{{d[j] = 8t[j]}}}
(1) {{{30 = 8*3.75}}}
(1) {{{30 = 30}}}
OK
and
(2) {{{d[r] = 4t[r]}}}
(2) {{{14 = 4*3.5}}}
(2) {{{14 = 14}}}
OK