Question 1067596
What is the head start in km for the bus?
{{{ d[1] = 60*2 }}}
{{{ d[1] = 120 }}} km
----------------------
Let {{{ t }}} = time in hrs for the taxi to overtake bus
Let {{{ d }}} = distance in km the taxi travel
until it overtakes the bus
Start a stopwatch when the taxi leaves
----------------------
Equation for bus:
(1) {{{ d - d[1] = 60t }}}
Equation for taxi:
(2) {{{ d = 80t }}}
----------------------
(1) {{{ d - 120 = 60t }}}
Substitute (2) into (1)
(1) {{{ 80t - 120 = 60t }}}
(1) {{{ 20t = 120 }}}
(1) {{{ t = 6 }}}
-----------------
The taxi overtakes the bus in 6 hrs
-----------------------------------
check:
(2) {{{ d = 80t }}}
(2) {{{ d = 80*6 }}}
(2) {{{ d = 480 }}} km
and
(1) {{{ d - 120 = 60t }}}
(1) {{{ d - 120 = 60*6 }}}
(1) {{{ d = 360 + 120 }}}
(1) {{{ d = 480 }}} km 
OK