Question 1150456
{{{ x }}} = circumference of rear wheel in meters
{{{ x - 6 }}} = circumference of front wheel in meters
Let {{{ 360/r }}} = meters traced on ground for
each revolution of the rear wheel
{{{ 360/( r + 10 ) }}} = meters traced on ground for
each revolution of the front wheel
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{{{ 360/r = x }}}
(1) {{{ r = 360/x }}}
and
{{{ 360/( r + 10 ) = x - 6 }}}
(2) {{{ r + 10 = 360/( x - 6 ) }}}
Plug (1) into (2)
(2) {{{ 360/x + 10 = 360/( x - 6 ) }}}
Multiply both sides by {{{ x*( x - 6 ) }}}
(2) {{{ 360*( x - 6 ) + 10x*( x - 6 ) = 360x }}}
(2) {{{ 360x - 2160 + 10x^2 - 60x = 360x }}}
(2) {{{ 10x^2 - 60x - 2160 = 0 }}}
(2) {{{ x^2 - 6x - 216 = 0 }}}
(2) {{{ ( x - 18 )*( x + 12 ) = 0 }}}
The circumference of the rear wheel is 18 m
{{{ x - 6 = 18 - 6 }}}
{{{ x - 6 = 12 }}}
The circumference of the front wheel is 12 m
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check answer:
(1) {{{ r = 360/x }}}
(1) {{{ r = 360/18 }}}
(1) {{{ r = 20 }}}
and
(2) {{{ r + 10 = 360/( x - 6 ) }}}
(2) {{{ r + 10 = 360/ 12 }}}
(2) {{{ r + 10 = 30 }}}
(2) {{{ r = 20 }}}
OK