Question 648758
First find the head start of the prop plane in miles
{{{ d[1] = 200*2 }}}
{{{ d[1] = 400 }}} mi
Start a stopwatch when the jet leaves
Now they will both fly for the same
amount of time until jet catches prop
Let {{{ d }}} = distance jet travels
Let {{{ t }}} = time on stopwatch
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Jet's equation:
(1) {{{ d = 550t }}}
prop's equation:
(2) {{{ d - 400 = 200t }}}
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Substitute (1) into (2)
(2) {{{ 550t - 400 = 200t }}}
(2) {{{ 350t = 400 }}}
(2) {{{ t = 8/7 }}} hrs
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(1) {{{ d = 550*(8/7) }}}
(1) {{{ d = 628.57 }}}
The planes are 628.57 mi from the start
( unless I miscalculated )