Question 655436
The bus has a head start  of {{{ 50*.5 = 25 }}} mi
Let {{{ d }}} = distance car travels until
it catches the bus
Let {{{ t }}} = time in hours car takes to catch bus
Start a stopwatch when the car leaves.
Car's equation:
(1) {{{ d = 60t }}}
Bus's equation:
(2) {{{ d - 25 = 50t }}}
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Substitute (1) into (2)
(2) {{{ 60t - 25 = 50t }}}
(2) {{{ 10t = 25 }}}
(2) {{{ t = 2.5 }}}
12:30 + 2.5 hrs = 3:00
The car catches the bus at 3:00 PM
check:
(1) {{{ d = 60*2.5 }}}
(1) {{{ d = 150 }}} mi
and
(2) {{{ d - 25 = 50*2.5 }}}
(2) {{{ d = 25 + 125 }}}
(2) {{{ d = 150 }}} mi
OK