# Suppose that during a test drive of two cars, one car travels 248 miles in the same time that the second car travels 200 miles. If the speed of one car is 12 miles per hour faster than the speed of the second car, how do you find the speed of both cars?

Oct 1, 2015

The first car is traveling at a speed of ${s}_{1} = 62$ mi/hr.
The second car is traveling at a speed of ${s}_{2} = 50$ mi/hr.

#### Explanation:

Let $t$ be the amount of time the cars are traveling

${s}_{1} = \frac{248}{t}$ and ${s}_{2} = \frac{200}{t}$

We are told:
${s}_{1} = {s}_{2} + 12$

That is
$\frac{248}{t} = \frac{200}{t} + 12$

$\Rightarrow 248 = 200 + 12 t$

$\Rightarrow 12 t = 48$

$\Rightarrow t = 4$

${s}_{1} = \frac{248}{4} = 62$

${s}_{2} = \frac{200}{4} = 50$