Question 1148283
Let {{{ t }}} = time in hrs for faster plane
to catch up with slower plane
Let {{{ d[1] }}} = the slower plane's head start in miles
Let {{{ d }}} = distance the faster plane travels until it
catches up with the slower plane
-----------------------------------------------------------
{{{ d[1] = 400*2 }}}
{{{ d[1] = 800 }}}
Equation for slower plane:
(1) {{{ d - 800 = 400t }}}
Equation for faster plane:
(2) {{{ d = 500t }}}
-----------------------------
Plug (2) into (1)
(1) {{{ 500t - 800 = 400t }}}
(1) {{{ 100t = 800 }}}
(1) {{{ t = 8 }}}
---------------------------
8 hrs after the faster plane leaves LAX they are traveling side by side
---------------------------
check:
(2) {{{ d = 500t }}}
(2) {{{ d = 500*8 }}}
(2) {{{ d = 4000 }}} mi
and
(1) {{{ d - 800 = 400t }}}
(1) {{{ d - 800 = 400*8 }}}
(1) {{{ d - 800 = 3200 }}}
(1) {{{ d = 4000 }}} mi
OK