# In the time that it takes one car to travel 93 km, a second car travels 111 km. If the average speed of the second car is 12 km/h faster than the speed of the first car, what is the speed of each car?

Aug 6, 2018

$\text{Car 1" \ = \ "64 km/h}$

$\text{Car 2" \ = \ "74 km/h}$

#### Explanation:

The formula for speed is

$s = \frac{d}{t}$

For the first car, we know $d$ and plugging it into the formula gives us

${s}_{1} = \frac{93}{t}$

We know the second car is $\text{12 km/h}$ faster and the distance is $\text{111 km}$, so the formula in terms of the first car's speed would be

${s}_{1} + 12 = \frac{111}{t} = {s}_{2}$

Now we can solve for ${s}_{1}$ in the second equation

${s}_{1} = \frac{111}{t} - 12$

Now we can set the two ${s}_{1}$ equal to each other and solve for $t$

$\frac{93}{t} = \frac{111}{t} - 12$

$93 = 111 - 12 t$

$12 t = 18$

$t = \frac{3}{2} \setminus \text{hours}$

Now we can plug $t$ into the first car equation to solve for the speed of it

${s}_{1} = \text{93 km"/(3/2 \ "h") = "62 km/h}$

We know the second car is $\text{12 km/h}$ faster, so

$\text{62 km/h" \ + \ "12 km/h" = "74 km/h}$