Question 1052086
I assume they take off at the same time.
Let {{{ s }}} = the speed in mi/hr of the slower plane
{{{ 1.5s }}} = the speed of the faster one
{{{ d }}} = distance in miles the faster one travels
{{{ d - 420 }}} = distance in miles the slower one travels
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Equation for slower one:
(1) {{{ d - 420 = s*8 }}}
Equation for faster one:
(2) {{{ d = 1.5s*8 }}}
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Substitute (2) into (1)
(1) {{{ 1.5*8s - 420 = 8s }}}
(1) {{{ 12s - 420 = 8s }}}
(1) {{{ 4s = 420 }}}
(1) {{{ s = 105 }}} mi
and
{{{ 1.5s = 157.5 }}} mi
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The speed in mi/hr of the slower plane is 105 mi/hr
The speed of the faster plane is 157.5 mi/hr
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check:
(1) {{{ d - 420 = 105*8 }}}
(1) {{{ d = 840 + 420 }}}
(1) {{{ d = 1260 }}} mi
and
(2) {{{ d = 1.5*105*8 }}}
(2) {{{ d = 1260 }}} mi
OK