Question 622266
Let {{{ s }}} = the speed of the slower driver in mi/hr
{{{ s + 15 }}} = the speed of the faster driver
Let {{{ d }}} = distance driven by slower driver
{{{ 37.5 - d }}} = distance driven by faster driver
{{{ .5 }}} hrs is the time for both drivers
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Slower driver's equation:
(1) {{{ d = s*(.5) }}}
Faster driver's equation:
(2) {{{ 37.5 - d = ( s + 15 )*(.5) }}}
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Substitute (1) into (2)
(2) {{{ 37.5 - d = ( s + 15 )*(.5) }}}
(2) {{{ 37.5 - .5s = ( s + 15 )*(.5) }}}
(2) {{{ 37.5 - .5s = .5s + 7.5 }}}
(2) {{{ s = 37.5 - 7.5 }}}
(2) {{{ s = 30 }}}
and
{{{ s + 15 = 45 }}}
The speed of the slower driver is 30 mi/hr
The speed of the faster driver is 45 mi/hr
check:
(1) {{{ d = s*(.5) }}}
(1) {{{ d = .5*30 }}}
(1) {{{ d = 15 }}} mi
and
(2) {{{ 37.5 - 15 = ( s + 15 )*(.5) }}}
(2) {{{ 22.5 = .5*( s + 15 ) }}}
(2) {{{ 45 = s + 15 }}}
(2) {{{ s = 30 }}}
OK