Question 982554
What distance is the truck's head start?
( 45 min is 3/4 of an hour )
{{{ d[1] = 90*(3/4) }}}
{{{ d[1] = 67.5 }}} km
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Start a stopwatch when the car leaves at 9:00
Let {{{ t }}} = time in hours on stopwatch when
car catches up with the truck
Let {{{ d }}} distance the car travels until it
catches up with the truck
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Equation for the car:
(1) {{{ d = 120t }}}
Equation for the truck:
(2) {{{ d - 67.5 = 90t }}}
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(1) {{{ t = d/120 }}}
(2) {{{ d - 67.5 = ( 90/120 )*d }}}
(2) {{{ d - 67.5 = .75d }}}
(2) {{{ .25d = 67.5 }}}
(2) {{{ d = 270 }}}
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They meet 270 km from Johannesburg
check:
(1) {{{ d = 120t }}}
(1) {{{ 270 = 120t }}}
(1) {{{ t = 2.25 }}}
and
(2) {{{ d - 67.5 = 90t }}}
(2) {{{ 270 - 67.5 = 90t }}}
(2) {{{ 202.5 = 90t }}}
(2) {{{ t = 2.25 }}}
OK
( note that they meet at 11:15 )