Question 953674
Let the speed of the slower car = {{{ s }}} mi/hr
The speed of the faster car = {{{ s + 7 }}} mi/hr
-----------------
The 1st to arrive at destination is the faster car
Equation for faster car:
(1) {{{ d = ( s + 7 )*5.5 }}}
Equation for slower car:
(2) {{{ 599.5 - d = s*5.5 }}}
-------------------------
(1) {{{ d = 5.5s + 38.5 }}}
(1) {{{ d - 5.5s = 38.5 }}}
and
(2) {{{ d + 5.5s = 599.5 }}}
-------------------------
Add the equations
{{{ 2d = 638 }}}
{{{ d = 319 }}}
The slower car has traveled
{{{ 599.5 - 319 = 280.5 }}}
The slower car has {{{ 319 - 280.5 = 38.5 }}} mi
left to reach destination
-----------------------
Equation for slower car:
(2) {{{ 599.5 - d = s*5.5 }}}
(2) {{{ 599.5 - 319 = s*5.5 }}}
(2) {{{ 280.5 = 5.5s }}}
(2) {{{ s = 51 }}}
-----------------
Find time for slower car to reach destination:
{{{ 38.5 = 51t }}}
{{{ t = .755 }}} hrs
convert to minutes:
{{{ t = 45.29 }}} min
To the nearest minutes, it takes 45 min
for slower car to arrive
----------------------
check:
For slower car:
{{{ .755 + 5.5 = 6.255 }}}
{{{ d[1] = 319 }}}
{{{ d[1] = s*6.255 }}}
{{{ 319 = 6.255s }}}
{{{ s = 50.999 }}}
This is close enough to {{{ s = 51 }}}
OK