carla and vicki left the house at the same time and began traveling down the same road in the same direction. Carla drove at a speed of 60 mph and vicki at a speed of 65 mph. how many hours was it before vicki was 20 miles ahead of carla?

Answer 1

Let's define the variables to set up the problem:
- Let \( t \) be the time in hours after they both left the house.

First, we need the distance formula, which states:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

Carla's distance after \( t \) hours is:
\[ \text{Distance}_{\text{Carla}} = 60t \]

Vicki's distance after \( t \) hours is:
\[ \text{Distance}_{\text{Vicki}} = 65t \]

We are asked to find the time \( t \) when Vicki is 20 miles ahead of Carla. Therefore, we set up the following equation based on the given information:
\[ \text{Distance}_{\text{Vicki}} - \text{Distance}_{\text{Carla}} = 20 \]

Substituting the distances we've calculated:
\[ 65t - 60t = 20 \]

Simplifying this equation:
\[ 5t = 20 \]

Solving for \( t \):
\[ t = \frac{20}{5} = 4 \]

Thus, it will take \( t = 4 \) hours for Vicki to be 20 miles ahead of Carla.