Question 1156786
Plane 1's head start is:
{{{ d[1] = 450*1 }}}
{{{ d[1] = 450 }}} mi
Start a stopwatch when plane 2 takes off
Let {{{ t }}} = time on stopwatch when
plane 2 catches plane 1
Let {{{ d }}} = plane 2 travels until it catches
plane 1
----------------------------
Plane 1 equation:
(1) {{{ d - 450 = 450t }}}
Plane 2 equation:
(2) {{{ d = 500t }}}
----------------------------
Plug (2) into (1)
(1) {{{ 500t - 450 = 450t }}}
(1) {{{ 50t = 450 }}}
(1) {{{ t = 9 }}}
It takes plane 2 9 hrs to catch plane 1
-------------------------
check:
(2) {{{ d = 500t }}}
(2) {{{ d = 500*9 }}}
(2) {{{ d = 4500 }}}
and
(1) {{{ d - 450 = 450t }}}
(1) {{{ d - 450 = 450*9 }}}
(1) {{{ d = 450*10 }}}
(1) {{{ d = 4500 }}}
OK