Final answer:
Brian sets off at 8:00 a.m. from Los Angeles to San Francisco at 50 mph, while Sarah leaves at 9:00 a.m. at 60 mph for the same destination. To find when Sarah catches up, we calculate Brian's lead when Sarah starts, which is 50 miles. Since Sarah travels 10 mph faster, she will catch up to Brian in 5 hours, which means at 2:00 p.m.
Step-by-step explanation:
In this mathematics problem, we are given a scenario where Brian and Sarah are both traveling from Los Angeles to San Francisco, a distance of 400 miles. Brian leaves at 8:00 a.m., traveling at a steady speed of 50 mph, while Sarah departs at 9:00 a.m., traveling at a steady 60 mph. To determine when Sarah catches up to Brian, we need to analyze their relative speeds and the time difference in their departures.
Here’s a step-by-step guide to solve the problem:
- Calculate the distance Brian has traveled by the time Sarah starts. Since Brian has a 1-hour head start, at 50 mph, he is 50 miles ahead.
- Since Sarah is traveling 10 mph faster than Brian, she reduces the lead by 10 miles every hour. The time taken to cover Brian's 50-mile lead traveling at 10 mph faster is the time it takes Sarah to catch up to Brian.
- Using the formula Time = Distance / Speed, we get Time = 50 miles / 10 mph = 5 hours.
- Therefore, Sarah will catch up to Brian at 2:00 p.m. if they maintain their steady speeds.
It is important to remember that this scenario assumes constant speeds and no stops or delays.