Typically these motion problems are used with a formula to calculate rate and time,
#d=rt#
You want to assign each plane its own little table to make things easier
plane 1 lets call it plane #F# for faster
and plane 2 let us call it #S# for slower
remember to define x as the time they will both be #1400# miles apart.
#F# - we are looking for the time so that is our variable #x#
#F# - we know the rate is 600mph
#S# - we are looking for the time so that is our variable #x#
#S# - lets assume this is a bigger plane that flies slower at #450mph#
#d = rt#
#F# =#600*x#
#S# =#450*x#
so now that we have rate and distance we can calculate the time.
#600x + 450x = 1400# (the amount they will be apart) and the equation to solve for the #x# (time)
#1050x = 1400#
now its as simple as solving for #x#
#(1050x)/1050 = 1400/1050#
simplify
#x = 4/3# convert to a mixed fraction because we need the time.
#1 1/3# what is #1/3# of an hour #1/3 #* #20/20= 20/60# so.. #20# minutes and an hour.
the planes will be #1400# miles apart at 1:20 pm
how long will they be apart at 1400 miles has become much easier because we have our time #x# figured out as #4/3#
#600(x)# or #600(4/3)# = #800#
#450(x)# or #450(4/3)# = #600#
this makes sense because if we add them together we get the distance #1400# our original distance. Hope this helps.
