maurice and rhonda are traveling in the same direction along the same road. maurice is traveling at 55 mph and is exactly 15 miles ahead of rhonda, who is traveling at 65 mph. How many hours will it take rhonda to catch maurice.

Question

(write your answer as a decimal)

Answer 1

To determine how many hours it will take Rhonda to catch Maurice, we need to consider the relative speeds and the initial distance between them.

Rhonda is traveling at 65 mph, and Maurice is traveling at 55 mph. So, Rhonda is gaining on Maurice at a rate of:
\[ 65 \text{ mph} - 55 \text{ mph} = 10 \text{ mph} \]

Maurice has a 15-mile head start. We need to find the time it takes for Rhonda to close this 15-mile gap at the rate at which she is gaining on him (\(10 \text{ mph}\)).

We can use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} \]

Plugging in the values:
\[ \text{Time} = \frac{15 \text{ miles}}{10 \text{ mph}} = 1.5 \text{ hours} \]

So, it will take Rhonda:
\[ 1.5 \text{ hours} \]

to catch up to Maurice.