Question 621342
Let {{{ a }}} = the speed of the car
Let {{{ b }}} = the speed of the train
Let {{{ t }}} = the time it takes for the
train to get to station B.
--------------------
Equation for the train:
(1) {{{ 220 = b*t }}}
Equation for the car:
(2) {{{ 220 = a*( t - 5.5 ) }}}
(3) {{{ a = 2b }}}
-------------
Substitute (3) into (2)
(2) {{{ 220 = 2b*( t - 5.5 ) }}}
and, from (1),
(1) {{{ t = 220/b }}}
Substitute this into (2)
(2) {{{ 220 = 2b*( 220/b - 5.5 ) }}}
(2) {{{ 220 = 440 - 11b }}}
(2) {{{ 11b = 220 }}}
(2) {{{ b = 20 }}}
and, since
(3) {{{ a = 2b }}}
(3) {{{ a = 40 }}}
The speed of the car is 40 mi/hr
The speed of the train is 20 mi/hr
check:
(1) {{{ 220 = 20t }}}
(1) {{{ t = 11 }}}
and
(2) {{{ 220 = 40*( t - 5.5 ) }}}
(2) {{{ 22/4 = t - 5.5 }}}
(2) {{{ 22 = 4t - 22 }}}
(2) {{{ 4t = 44 }}}
(2) {{{ t = 11 }}}
OK