# 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?

Oct 28, 2015

John drives $30$ miles per hour

#### Explanation:

Let
$\textcolor{w h i t e}{\text{XXX}} J =$ John's driving speed (in miles per hour)
$\textcolor{w h i t e}{\text{XXX}} G =$ Georges' driving speed (in miles per hour)

For a certain amount of time, $t$, we are told:
[1]$\textcolor{w h i t e}{\text{XXX}} t = \frac{240}{J}$
[2]$\textcolor{w h i t e}{\text{XXX}} t = \frac{200}{G}$
and also that
[3]$\textcolor{w h i t e}{\text{XXX}} J = G + 5$
$\Rightarrow$[4]$\textcolor{w h i t e}{\text{XXX}} G = J - 5$

Combining [1] and [2]
[5]$\textcolor{w h i t e}{\text{XXX}} \frac{240}{J} = \frac{200}{G}$
$\Rightarrow$[6]$\textcolor{w h i t e}{\text{XXX}} 200 J = 240 G$

Substituting $\left(J - 5\right)$ from [4] for $G$ in [6]
[7]$\textcolor{w h i t e}{\text{XXX}} 200 J = 240 \left(J - 5\right)$
$\Rightarrow$[8]$\textcolor{w h i t e}{\text{XXX}} 200 J = 240 J - 1200$
$\Rightarrow$[9]$\textcolor{w h i t e}{\text{XXX}} 40 J = 1200$
$\Rightarrow$[10]$\textcolor{w h i t e}{\text{XXX}} J = 30$