Final answer:
To determine when Ariel's brother will catch up with her, we calculate the distance Ariel is covered by the time her brother starts and use the relative speed to find the time needed for her brother to catch up. Ariel's brother will catch up at 5 p.m.
Step-by-step explanation:
The question asks us to determine the time at which Ariel's brother catches up with her after both have set off from the same point at different times and speeds. This problem involves the concepts of distance, speed, and time, which are fundamental to understanding motion in physics, but it is presented as a Mathematics problem.
Ariel begins her journey at 9 a.m. driving at 45 mph. Her brother sets off at 11 a.m., traveling at 60 mph. When Ariel's brother leaves, Ariel has already been traveling for 2 hours. To find out when her brother will catch up, we first need to calculate the distance Ariel has covered by 11 a.m.:
• Distance = Speed × Time
• Distance = 45 mph × 2 hours
• Distance = 90 miles
Ariel's brother needs to cover this 90-mile gap to catch up. Since they are traveling in the same direction, we can calculate the time it will take for her brother to catch up by using the relative speed between them:
• Relative speed = Brother's speed - Ariel's speed
• Relative speed = 60 mph - 45 mph
• Relative speed = 15 mph
• Time to catch up = Distance / Relative speed
• Time to catch up = 90 miles / 15 mph
• Time to catch up = 6 hours
Since Ariel's brother started at 11 a.m., we added these 6 hours to find the catch-up time:
• 11 a.m. + 6 hours = 5 p.m.
Ariel's brother will catch up with her at 5 p.m.