Alice leaves her house, driving east at 45 miles per hour (mph). Thirty minutes later her husband Dave notices she forgot her cell phone and sets off after her. How fast must Dave travel in order to catch up with Alice 3 hours after he leaves?

• A. 49 mph
• B. 50.5 mph
• C. 52.5 mph
• D. 54 mph

Answer: (C)

To determine how fast Dave must travel to catch up with Alice, we first need to understand the distances each person travels.

Alice leaves her house and drives east at a speed of 45 mph for a total of 3.5 hours before Dave catches up with her. This is because she starts 30 minutes (or 0.5 hours) earlier than Dave. Therefore, the time Alice drives before they meet is:

• Total time for Alice: 3 hours (the time after Dave starts driving) + 0.5 hours (the time before Dave starts) = 3.5 hours.

Calculating the distance Alice travels:

Distance = Speed × Time

Distance = 45 mph × 3.5 hours = 157.5 miles.

Now, let's consider Dave. He starts driving after Alice and has 3 hours to catch up. The distance Dave needs to travel is the same as the distance Alice has already covered, which is 157.5 miles.

To find out how fast Dave needs to drive to cover this distance in 3 hours, we use the formula:

Speed = Distance / Time

Speed = 157.5 miles / 3 hours = 52.5 mph.

Thus, if Dave