Question 269593
Write equations for each:
{{{d[1] = r[1]*t[1]}}}
{{{d[2] = r[2]*t[2]}}}
given:
{{{t[1] = 5}}} hrs
{{{t[2] = 5}}} hrs
{{{r[2] = r[1] + 10}}} mi/hr
{{{d[1] + d[2] = 550}}} mi
-----------------------
(1) {{{d[1] = r[1]*t[1]}}}
(1) {{{d[1] = r[1]*5}}}
(1) {{{5r[1] - d[1] = 0}}}
-----------------------
(2) {{{d[2] = r[2]*t[2]}}}
(2) {{{550 - d[1] = (r[1] + 10)*5}}}
(2) {{{550 - d[1] = 5r[1] + 50}}}
(2) {{{5r[1] + d[1] = 500}}}
------------------------
Add (1) and (2)
(1) {{{5r[1] - d[1] = 0}}}
(2) {{{5r[1] + d[1] = 500}}}
{{{10r[1] = 500}}}
{{{r[1] = 50}}} mi/hr
And, since
{{{r[2] = r[1] + 10}}}
{{{r[2] = 50 + 10}}}
{{{r[2] = 60}}} mi/hr
The 1st car goes 50 mi/hr, the 2nd car goes 60 mi/hr
check:
(2) {{{550 - d[1] = (r[1] + 10)*5}}}
(2) {{{550 - d[1] = (50 + 10)*5}}}
(2) {{{550 - d[1] = 300}}}
(2) {{{d[1] = 250}}} mi
and
(2) {{{d[2] = r[2]*5}}}
(2) {{{d[2] = 60*5}}}
(2) {{{d[2] = 300}}}
and
{{{d[1] + d[2] = 550}}}
OK