Question 639510
I think they are also assuming they are both
going at top speed the whole time
Let {{{ s }}} = the speed of the faster car in km/hr
Let {{{ d }}} = distance in km the slower car travels in 1/2 hr
Equation for the slower car:
(1) {{{ d = (9/10)*s*(1/2) }}}
Equation for faster car:
(2) {{{ d + 10 = s*(1/2) }}} 
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Multiply both sides of (1) by {{{20}}}
(1) {{{ 20d = 9s }}}
(1) {{{ d = (9/20)*s }}}
Substitute this into (2)
(2) {{{ (9/20)*s + 10 = s*(1/2) }}}
(2) {{{ 9s + 200 = 10s }}}
(2) {{{ s = 200 }}}
{{{ (9/10)*s = (9/10)*200 }}}
{{{ (9/10)*s = 180 }}}
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The speed of the faster car is 200 km/hr
The speed of the slower car is 180 km/hr
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check:
(1) {{{ d = (9/10)*s*(1/2) }}} 
(1) {{{ d = 180*(1/2) }}}
(1) {{{ d = 90 }}} km
and
(2) {{{ d + 10 = 200*(1/2) }}}  
(2) {{{ d = 100 - 10 }}}
(2) {{{ d = 90 }}} km
OK