4.

Question

Carlos and Maria drove a total of 191 miles in 3.8 hours. Carlos drove the first part of the trip and averaged 49 miles per hour. Maria drove the remainder of the trip and averaged 52 miles per hour. For approximately how many hours did Maria drive? Round your answer to the nearest tenth if necessary.

Answer 1

Let \( t_C \) be the time (in hours) that Carlos drove, and \( t_M \) be the time (in hours) that Maria drove.

From the problem, we know the following:

1. The total time driven by both is: \[ t_C + t_M = 3.8 \]

2. The total distance driven is 191 miles, which can be expressed using their average speeds: \[ 49t_C + 52t_M = 191 \]

Now we have a system of two equations:

1. \( t_C + t_M = 3.8 \)
2. \( 49t_C + 52t_M = 191 \)

We can solve for \( t_C \) in terms of \( t_M \) using the first equation: \[ t_C = 3.8 - t_M \]

Now, substitute \( t_C \) in the second equation: \[ 49(3.8 - t_M) + 52t_M = 191 \]

Distributing \( 49 \): \[ 186.2 - 49t_M + 52t_M = 191 \]

Combine like terms: \[ 186.2 + 3t_M = 191 \]

Now, isolate \( t_M \): \[ 3t_M = 191 - 186.2 \] \[ 3t_M = 4.8 \] \[ t_M = \frac{4.8}{3} = 1.6 \]

Therefore, Maria drove for approximately \( 1.6 \) hours.

Rounding to the nearest tenth, Maria drove for \( \boxed{1.6} \) hours.