# Carlos and Maria have drove a total of 197 miles in 3.8 hours. Carlos drove the first part of the trip and averaged 55 miles per hour. Maria drove the remainder of the trip and averaged 47 miles per hour. For approximately how many hours did Maria drive?

May 6, 2018

Maria drove for $1.5$ hours.

#### Explanation:

($x = \text{hours that Carlos drove", y="hours that Maria drove}$)

We know that:
$55 \cdot x + 47 \cdot y = 197$
$x + y = 3.8$

$| \left(55 \cdot x + 47 \cdot y = 197\right) , \left(x + y = 3.8 | - y\right) |$

$| \left(55 \cdot x + 47 \cdot y = 197\right) , \left(\textcolor{red}{x = 3.8 - y}\right) |$

$55 \cdot \textcolor{red}{\left(3.8 - y\right)} + 47 \cdot y = 197$
$209 - 55 y + 47 y = 197 | - 209$
-8y=-12|:(-8)
$y = \frac{3}{2}$