Question 887356
The difference in their ages will always be {{{ 6 }}} years
Let {{{ d }}} = Dandy's age in 2000
Let {{{ n }}} = Noel's age in 2000
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(1) {{{ d - n = 6 }}}
(2) {{{ d = 4n + 2 }}}
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(1) {{{ d = n + 6 }}}
Substitute (1) into (2)
(2) {{{ n + 6 = 4n + 2 }}}
(2) {{{ 3n = 6 - 2 }}}
(2) {{{ 3n = 4 }}}
(2) {{{ n = 4/3 }}}
and
(1) {{{ d = 4/3 + 6 }}}
(1) {{{ d = 22/3 }}}
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Noel will be {{{ 4/3 + 20 = 64/3 }}}
{{{ 64/3 = 21 + 1/3 }}} 
Noel will be 21 and 4 months
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check:
(2) {{{ d = 4n + 2 }}}
(2) {{{ 22/3 = 4*( 4/3 ) + 2 }}}
(2) {{{ 22/3 = 16/3 + 6/3 }}}
(2) {{{ 22/3 = 22/3 }}}
OK