Question 771600
Their velocities add when they are going
in opposite directions, and their velocities
subtract when they are going in the same direction
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In the 1st case, think of one cyclist as standing still
and the other one traveling at the sum of their speeds
In the 2nd case, think of one cyclist as standing still
and the other one traveling at the difference of their speeds
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Let {{{ s[1] }}} = the speed of the slower cyclist
Let {{{ s[2] }}} = the speed of the faster cyclist
(1) {{{ 87 = ( s[1] + s[2] )*3 }}} 
(2) {{{ 9 = ( s[1] - s[2] )*3 }}}
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(1) {{{ s[1] + s[2] = 29 }}}
(2) {{{ s[1] - s[2] = 3 }}}
Add the equations
{{{ 2s[1] = 32 }}}
{{{ s[1] = 16 }}}
and, since
(2) {{{ s[1] - s[2] = 3 }}}
(2) {{{ 16 - s[2] = 3 }}}
(2) {{{ s[2] = 13 }}}
Their speeds are 16 km/hr and
13 km/hr
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check:
(1) {{{ 87 = ( s[1] + s[2] )*3 }}} 
(1) {{{ 87 = ( 16 + 13 )*3 }}} 
(1) {{{ 87 = 29*3 }}}
(1) {{{ 87 = 87 }}}
OK