Question 1042682
Let {{{ s[1] }}} = the speed of the private jet in mi/hr
Let {{{ s[2] }}} = the speed of the commercial jet in mi/hr
given:
(1) {{{ s[2] = 2*s[1] - 110 }}}
Let {{{ d }}} = distance flown by both planes
------------------------------------
(2) {{{ d = s[1]*13 }}}
(3) {{{ d = s[2]*9 }}}
------------------
From (2) and (3):
{{{ 13s[1] = 9s[2] }}}
{{{ s[2] = (13/9)*s[1] }}}
-------------------
Plug this last result into (1)
(1) {{{ s[2] = 2*s[1] - 110 }}}
(1) {{{ (13/9)*s[1] = 2*s[1] - 110 }}}
(1) {{{ 13s[1] = 18s[1] - 990 }}}
(1) {{{ 5s[1] = 990 }}}
(1) {{{ s[1] = 198 }}}
and
{{{ s[2] = (13/9)*s[1] }}}
{{{ s[2] = (13/9)*198 }}}
{{{ s[2] = 13*22 }}}
{{{ s[2] = 286 }}}
The speed of the private jet is 198 mi/hr
The speed of the commercial jet is 286 mi/hr
-----------------------
check:
(1) {{{ s[2] = 2*s[1] - 110 }}}
(1) {{{ 286 = 2*198 - 110 }}}
(1) {{{ 286 = 396 - 110 }}}
(1) {{{ 286 = 286 }}}
OK
(2) {{{ d = s[1]*13 }}}
(2) {{{ d = 198*13 }}}
(2) {{{ d = 2574 }}}
and 
(3) {{{ d = s[2]*9 }}}
(3) {{{ d = 286*9 }}}
(3) {{{ d = 2574 }}}
OK