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?

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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?

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Answer 1 · 2015-10-28T10:20:21

John drives $30$ $30$ miles per hour

Explanation:

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

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

Combining [1] and [2]
[5] $XXX \frac{240}{J} = \frac{200}{G}$ $color(white)("XXX")240/J=200/G$
$\Rightarrow$ $rArr$ [6] $XXX 200 J = 240 G$ $color(white)("XXX")200J=240G$

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

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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?

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