John can drive 240miles at the same time as it takes george to drive 220 miles if john drives 5mph faster than george then how fast does john drive?

1 Answer
Alan P.
Oct 28, 2015

John drives #30# miles per hour

Explanation:

Let
#color(white)("XXX")J = # John's driving speed (in miles per hour)
#color(white)("XXX")G = # Georges' driving speed (in miles per hour)

For a certain amount of time, #t#, we are told:
[1]#color(white)("XXX")t=240/J#
[2]#color(white)("XXX")t=200/G#
and also that
[3]#color(white)("XXX")J=G+5 #
#rArr#[4]#color(white)("XXX")G=J-5#

Combining [1] and [2]
[5]#color(white)("XXX")240/J=200/G#
#rArr#[6]#color(white)("XXX")200J=240G#

Substituting #(J-5)# from [4] for #G# in [6]
[7]#color(white)("XXX")200J=240(J-5)#
#rArr#[8]#color(white)("XXX")200J=240J-1200#
#rArr#[9]#color(white)("XXX")40J=1200#
#rArr#[10]#color(white)("XXX")J=30#

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