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# One car travels 270 miles in the same amount of time it takes a second car traveling 6 miles per hour slower than the first to go 234 miles. What are the speeds of the cars?

Feb 9, 2018

#### Answer:

Car one speed is x, and car 2 speed is x-6
Both cars travel same amount of time. d= v x t so t= d/v
set the two times equal and solve for x

#### Explanation:

$\frac{270}{x} = \frac{234}{x - 6}$

$270 \left(x - 6\right) = 234 x$

$270 x - 1620 = 234 x$

$36 x - 1620 = 0$

$36 x = 1620$

$x = 45 m p h$

Feb 9, 2018

#### Answer:

$45 \text{ mph and "39" mph}$

#### Explanation:

$\text{using the formula}$

• " average speed (S)"="distance (D)"/"time (T)"

$T \text{ is a constant quantity here}$

$\textcolor{b l u e}{\text{car 1}}$

$S = \frac{270}{T} \Rightarrow S T = 270 \to \left(1\right)$

$\textcolor{b l u e}{\text{car 2}}$

$S - 6 = \frac{234}{T} \Rightarrow S T - 6 T = 234 \to \left(2\right)$

$\text{subtract } \left(2\right) - \left(1\right)$

$\Rightarrow 6 T = 270 - 234 = 36$

$\Rightarrow T = \frac{36}{6} = 6 \text{ hours}$

$\Rightarrow \textcolor{b l u e}{\text{car 1"toS=270/6=45" mph}}$

$\Rightarrow \textcolor{b l u e}{\text{car 2 "toS=234/6=39" mph}}$