Subjects algebra

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1. **Problem statement:** Lauren wants to arrive at station B by 12:00 on Thursday. Each bus takes 48 minutes to travel from station A to station B. It takes Lauren 13 minutes to get from her house to station A. We need to find the latest time Lauren can leave her house to catch a bus that gets her to station B by 12:00. 2. **Understanding the problem:** - Travel time from station A to B is 48 minutes. - Lauren must arrive at station B by 12:00. - Therefore, the bus must leave station A at or before $$12:00 - 48\text{ minutes} = 11:12.$$ - Lauren needs 13 minutes to get from her house to station A, so she must leave her house at or before $$\text{bus departure time} - 13\text{ minutes}.$$ 3. **Find the latest bus departure time on Thursday (a weekday) at or before 11:12:** From the Monday to Friday timetable for hour 11, the bus departure times are 02, 19, 35, 52 minutes past 11. - Times: 11:02, 11:19, 11:35, 11:52 - Only 11:02 is before or equal to 11:12. 4. **Calculate the latest time Lauren can leave her house:** - Bus departure time: 11:02 - Subtract 13 minutes to get the latest time Lauren can leave her house: $$11:02 - 0:13 = 10:49.$$ 5. **Final answer:** Lauren must leave her house by **10:49** at the latest to catch the bus that arrives at station B by 12:00 on Thursday.