Question 625519
The truck has a head start of 
{{{ d[1] = 40*2 }}}
{{{ d[1] = 80 }}} mi
Start a stopwatch when the bus leaves
First I'll find out when the bus catches up
with the truck
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Equation for the bus:
(1) {{{ d[2] = 60t }}}
Equation for the truck:
(2) {{{ d[2] - 80 = 40t }}}
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(2) {{{ d[2] = 40t + 80 }}}
Substitute (1) into (2)
(2) {{{ 60t = 40t + 80 }}}
(2) {{{ 20t = 80 }}}
(2) {{{ t = 4 }}} hrs
and
(1) {{{ d[2] = 60t }}}
(1) {{{ d[2] = 60*4 }}}
(1) {{{ d[2] = 240 }}} mi
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Now the truck continues on  for distance = 
{{{ d[3] }}} mi
During this time the bus must travel
{{{ d[3] + 20 }}} mi
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Equation for bus:
(1) {{{ d[3] + 20 = 60t }}}
Equation for truck:
(2) {{{ d[3] = 40t }}}
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substitute (2) into (1)
(1) {{{ 40t + 20 = 60t }}}
(1) {{{ 20t = 20 }}}
(1) {{{ t = 1 }}} hr
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The elapsed time on the stop watch is
{{{ 4 + 1 = 5 }}}
The bus gets 20 mi ahead of the truck in 5 hrs
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check answer:
The total distance for the bus is
{{{ d[2] + d[3] + 20 = 240 + 40 + 20 }}}
{{{ d[2] + d[3] + 20 = 300 }}} mi
The total distance for the truck is 
{{{ d[2] - 80 + d[3] = 80 + 240 - 80 + 40 }}}
{{{ d[2] - 80 + d[3] = 280 }}}
Equation for bus:
{{{ 300 = 60t }}}
{{{ t = 5 }}} hrs
Equation for truck:
{{{ 200 = 40t }}}
{{{ t = 5 }}} hrs 
OK