Question

Alan leaves Los Angeles at 8:00 a.m. to drive to San Francisco, 400 mi away. He travels at a steady 46.0 mph. Beth leaves Los Angeles at 9:00 a.m. and drives at a steady 56.0 mph. At what time will Beth catch up to Alan?

Answer 1

By calculating the head start and relative speeds of Alan and Beth, we determined that Beth will catch up to Alan at approximately 1:36 p.m.

Step-by-step explanation:

To determine at what time Beth will catch up to Alan, we need to calculate the distance each has traveled by the time they meet and equalize their respective distances.

Step-by-Step Calculation

Alan's head start: By the time Beth starts at 9:00 a.m., Alan has already been traveling for 1 hour at 46 mph. So Alan's head start is 46 miles.

Relative speed: Since both are traveling in the same direction, to find out how quickly Beth is catching up to Alan, we subtract Alan's speed from Beth's speed. Thus, Beth's relative speed is Beth's speed - Alan's speed = 56 mph - 46 mph = 10 mph.

Time to catch up: To find out how long it will take Beth to catch up, we divide the distance of Alan's head start by the relative speed. The time Beth will take to catch up is 46 miles / 10 mph = 4.6 hours.

Catch up time: Beth started at 9:00 a.m., so she will catch up to Alan at 9:00 a.m. + 4.6 hours. Therefore, Beth will catch up to Alan at approximately 1:36 p.m. (since 0.6 hours = 36 minutes).