Question

1. michael wants to visit a museum that opens at 8:30 on fridays. it is located near the ridc east bus stop. what time should michael leave the natrona heights bus stop near his home to arrive at the museum as close to opening time as possible? refer to the bus schedules below.

p10 allegheny valley flyer
monday through friday service
to downtown pittsburgh
bus stop names and corresponding times table (to downtown pittsburgh)
monday through friday service
to tarentum - natrona heights
bus stop names and corresponding times table (to tarentum - natrona heights)

Explanation:

Step1: Identify relevant bus schedules

We need to find the bus that departs from Natrona Heights (Michael's home stop) and arrives at RIDC East (near the museum) as close to 8:30 as possible. We look at the "To Downtown Pittsburgh" schedule (since the museum is on the way to Downtown from Natrona Heights) for the Natrona Heights stop and RIDC East stop.

Step2: Find departure and arrival times

- For Natrona Heights stop (To Downtown Pittsburgh schedule): Let's list the departure times from Natrona Heights and corresponding arrival times at RIDC East.
- Departure from Natrona Heights: 5:18, 5:38, 5:58, 6:13, 6:25, 6:40, 6:55, 7:15, 7:45
- Corresponding arrival at RIDC East: 6:01, 6:21, 6:41, 6:56, 7:08, 7:23, 7:38, 7:58, 8:28
- We need the arrival at RIDC East to be as close to 8:30 as possible. The arrival time 8:28 is the closest before 8:30? Wait, no, wait. Wait, the museum opens at 8:30. Wait, maybe we made a mistake. Wait, the "To Downtown Pittsburgh" is going towards Downtown, so the direction from Natrona Heights to RIDC East is towards Downtown. Wait, but maybe we should check the other schedule? No, the first schedule is To Downtown, so Natrona Heights is a stop before RIDC East in that direction. Wait, let's check the times again. Wait, the last departure from Natrona Heights in the To Downtown schedule is 7:45, arriving at RIDC East at 8:28. But is there a later bus? Wait, no, the last row is 7:34 from Harrison, 7:37 from Freeport at Oak Manor Dr, 7:45 from Natrona Heights, 7:47 from Freeport at Alabama Ave, 7:55 from Tarentum, 7:59 from 4th Ave at Park and Ride, 8:09 from Springdale, 8:11 from Cheswick, 8:17 from Harmar Dr, 8:28 from RIDC East? Wait, no, the columns are from left (Harrison) to right (Downtown). So Natrona Heights is a column, RIDC East is a later column (to the right). So the departure time from Natrona Heights is the time when the bus leaves Natrona Heights, and then arrives at RIDC East later. So let's list the departure times from Natrona Heights (To Downtown) and arrival at RIDC East:
- Departure: 5:18 → Arrival: 6:01
- 5:38 → 6:21
- 5:58 → 6:41
- 6:13 → 6:56
- 6:25 → 7:08
- 6:40 → 7:23
- 6:55 → 7:38
- 7:15 → 7:58
- 7:45 → 8:28
- Now, the museum opens at 8:30. So we need the arrival at RIDC East as close to 8:30 as possible, either before or after, but preferably before or just after. The arrival time 8:28 is 2 minutes before 8:30. Is there a bus that arrives after 8:30? Wait, no, the last arrival at RIDC East in the To Downtown schedule is 8:28. Wait, maybe we looked at the wrong schedule. Wait, the second schedule is To Tarentum - Natrona Heights, which is the reverse direction (from Downtown to Natrona Heights). So that's not useful for Michael, who is leaving Natrona Heights to go to RIDC East (towards Downtown). So the only arrival at RIDC East from Natrona Heights (To Downtown) is up to 8:28. Wait, but maybe we made a mistake. Wait, let's check the time of the last bus. Wait, the bus that departs Natrona Heights at 7:45 arrives at RIDC East at 8:28. So Michael should leave Natrona Heights at 7:45 to arrive at RIDC East at 8:28, which is 2 minutes before the museum opens at 8:30. Is there a bus that departs later from Natrona Heights? No, the last departure from Natrona Heights in the To Downtown schedule is 7:45. Wait, but maybe we misread the schedule. Let's check the columns again. The columns are:

Harrison → Bakerstown Rd at Alter Rd (BP) → Harrison → Freeport Rd opp Oak Manor Dr → Natrona Heights → Freeport Rd at Alabama Ave → Brackenridge → Ninth Ave past Penn St → Tarentum → 4th Ave at Park and Ride → Creighton → Freeport Rd at Bailey’s Run Rd → Springdale → Pittsburgh St at Colfax St → Cheswick → Pittsburgh St past Highland Ave → Harmar → Alpha Dr at Harmar Park - and - Ride → RIDC East Rt 28 Expwy Ramp at Gamma Dr → Larimer → Washington Blvd at Frankstown Ave → East Liberty East Liberty Station → Downtown Penn Station → Downtown Liberty Ave at Gateway #4

So Natrona Heights is the 5th column (after Freeport Rd opp Oak Manor Dr), RIDC East is the 16th column (before Larimer). So the time at Natrona Heights is the departure time from Natrona Heights, and the time at RIDC East is the arrival time there. So let's list the times row by row:

Row 1: 5:08 (Harrison) →... → 5:18 (Natrona Heights) →... → 6:01 (RIDC East)
Row 2: 5:28 →... → 5:38 →... → 6:21
Row 3: 5:48 →... → 5:58 →... → 6:41
Row 4: 6:03 →... → 6:13 →... → 6:56
Row 5: 6:14 →... → 6:25 →... → 7:08
Row 6: 6:29 →... → 6:40 →... → 7:23
Row 7: 6:44 →... → 6:55 →... → 7:38
Row 8: 7:04 →... → 7:15 →... → 7:58
Row 9: 7:34 →... → 7:45 →... → 8:28

So the last bus from Natrona Heights (To Downtown) departs at 7:45 and arrives at RIDC East at 8:28, which is 2 minutes before the museum opens at 8:30. Is there a bus that departs later from Natrona Heights? No, because the next row would be later, but the last row is the 9th row with 7:34, 7:37, 7:45, etc. So the departure time from Natrona Heights is 7:45, arriving at RIDC East at 8:28, which is the closest to 8:30 (2 minutes early). So Michael should leave Natrona Heights at 7:45. Wait, but let's confirm. The question is "What time should Michael leave the Natrona Heights bus stop near his home to arrive at the museum as close to opening time as possible?" So the museum opens at 8:30, so we need the arrival at RIDC East (near the museum) to be as close to 8:30 as possible. The arrival time 8:28 is 2 minutes before 8:30. Is there a bus that arrives after 8:30? Let's check the reverse direction? No, the reverse direction is To Tarentum - Natrona Heights, which is going from Downtown to Natrona Heights, so that's not useful for Michael (he needs to go from Natrona Heights to RIDC East, towards Downtown). So the only possible bus is the one departing Natrona Heights at 7:45, arriving at RIDC East at 8:28. Wait, but maybe we made a mistake in the direction. Wait, maybe the RIDC East is in the opposite direction? No, the first schedule is To Downtown, so Natrona Heights is west of RIDC East, and the bus is going east towards Downtown, so RIDC East is east of Natrona Heights, so the bus leaves Natrona Heights and goes to RIDC East (eastward). So the departure time from Natrona Heights is 7:45, arrival at RIDC East at 8:28. So that's the latest bus that arrives before 8:30. Wait, but 8:28 is 2 minutes before 8:30. Is there a bus that arrives after 8:30? Let's check the last row: the time at RIDC East in the last row is 8:28? Wait, no, the last row's RIDC East time is 8:28? Wait, the last row (9th row) has:

Harrison: 7:34

Bakerstown Rd at Alter Rd (BP): 7:37

Harrison: (wait, no, the first column is Harrison, then Bakerstown Rd at Alter Rd (BP), then Harrison (Freeport Rd), then Freeport Rd opp Oak Manor Dr, then Natrona Heights, etc. Wait, maybe the columns are:

1. Harrison

2. Bakerstown Rd at Alter Rd (BP)

3. Harrison (Freeport Rd)

4. Freeport Rd opp Oak Manor Dr

5. Natrona Heights

6. Freeport Rd at Alabama Ave

7. Brackenridge

8. Ninth Ave past Penn St

9. Tarentum

10. 4th Ave at Park and Ride

11. Creighton

12. Freeport Rd at Bailey’s Run Rd

13. Springdale

14. Pittsburgh St at Colfax St

15. Cheswick

16. Pittsburgh St past Highland Ave

17. Harmar

18. Alpha Dr at Harmar Park - and - Ride

19. RIDC East Rt 28 Expwy Ramp at Gamma Dr

20. Larimer

21. Washington Blvd at Frankstown Ave

22. East Liberty East Liberty Station

23. Downtown Penn Station

24. Downtown Liberty Ave at Gateway #4

So row 9:

Column 1 (Harrison): 7:34

Column 2: 7:37

Column 3: (Harrison Freeport Rd):? Wait, maybe the original schedule has rows as different bus trips. Each row is a different bus. So row 1: first bus, row 2: second bus, etc. So row 9 is the 9th bus of the day. So departure from Natrona Heights (column 5) in row 9 is 7:45, and arrival at RIDC East (column 19) in row 9 is 8:28. So that's the time. So Michael should leave Natrona Heights at 7:45 to arrive at RIDC East at 8:28, which is 2 minutes before the museum opens at 8:30.

Answer:

Michael should leave the Natrona Heights bus stop at 7:45.