Question

1. marcy wants to catch the bus at 3 : 45 from the east liberty bus stop to go to a store near the brackenridge bus stop. she plans to catch the bus back to the east liberty bus stop as close to an hour after she arrives at the brackenridge stop as possible. what time will she arrive back to the east liberty bus stop?

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

Explanation:

Step1: Find arrival time at Brackenridge

Marcy catches the bus at East Liberty (Stop B) at 3:45 (from the "To Tarentum - Natrona Heights" schedule). We need to find when she arrives at Brackenridge. Looking at the "To Tarentum - Natrona Heights" schedule, the column for Brackenridge (Ninth Penn Ave) has a time of 4:39 for the 3:45 departure from East Liberty. Wait, no, wait: actually, the "To Tarentum - Natrona Heights" is the return direction? Wait, no, first, she is going from East Liberty (3:45) to Brackenridge. Wait, the first schedule is "To Downtown Pittsburgh" (morning/afternoon going to downtown), the second is "To Tarentum - Natrona Heights" (returning from downtown). Wait, Marcy wants to go from East Liberty to Brackenridge (to the store) and then back. So first, she takes the bus from East Liberty (East Liberty Stop B) at 3:45 (from the "To Tarentum - Natrona Heights" schedule? No, wait, the "To Downtown Pittsburgh" schedule has East Liberty at 6:15, 6:35, etc. Wait, no, the second schedule is "To Tarentum - Natrona Heights" which is the direction from Downtown to Tarentum, so East Liberty (Stop B) has a departure at 3:45 (going towards Tarentum, which would be away from Downtown, so towards Brackenridge? Wait, the stops in "To Tarentum - Natrona Heights" go from Downtown to Tarentum, so East Liberty is a stop, then Larimer, then RIDC, etc., then Brackenridge. So the departure from East Liberty (Stop B) is 3:45, and the arrival at Brackenridge (Ninth Penn Ave) is 4:39 (looking at the "To Tarentum - Natrona Heights" schedule, the row with 3:45 at East Liberty, then the Brackenridge column: 4:39). Wait, no, let's check the times. The "To Tarentum - Natrona Heights" schedule: the first row is 3:30 at Downtown Liberty Ave, 3:39 at Downtown Penn Station B, 3:45 at East Liberty Stop B, 3:49 at Larimer, 4:02 at RIDC, 4:11 at Harmar, 4:17 at Cheswick, 4:20 at Springdale, 4:28 at Creighton, 4:34 at Tarentum, 4:39 at Brackenridge. Yes, so she departs East Liberty at 3:45, arrives at Brackenridge at 4:39.

Step2: Find return bus time (1 hour after arrival)

She arrives at Brackenridge at 4:39. She wants to catch the bus back as close to an hour later, so 4:39 + 1 hour = 5:39. Now, we need to find the bus from Brackenridge back to East Liberty (in the "To Downtown Pittsburgh" schedule, since that's the direction back to East Liberty). The "To Downtown Pittsburgh" schedule has Brackenridge (Ninth Penn Ave) with times: 5:20, 5:40, 6:00, 6:15, 6:27, 6:42, 6:57, 7:17, 7:47. Wait, no, the "To Downtown Pittsburgh" schedule's Brackenridge column (Ninth Penn Ave past) has times: 5:20, 5:40, 6:00, 6:15, 6:27, 6:42, 6:57, 7:17, 7:47. Wait, we need the time at Brackenridge (Ninth Penn Ave) in the "To Downtown Pittsburgh" schedule (going towards Downtown, which would pass East Liberty). So we need to find the bus that departs Brackenridge as close to 5:39 as possible. Let's look at the "To Downtown Pittsburgh" schedule, Brackenridge column (Ninth Penn Ave past):

Looking at the rows:

First row: 5:20 (Brackenridge), 5:28 (Tarentum), 5:32 (Creighton), etc.

Second row: 5:40 (Brackenridge), 5:48 (Tarentum), 5:52 (Creighton), etc.

Third row: 6:00 (Brackenridge), 6:08 (Tarentum), 6:12 (Creighton), etc.

Wait, the times at Brackenridge in "To Downtown Pittsburgh" are 5:20, 5:40, 6:00, 6:15, 6:27, 6:42, 6:57, 7:17, 7:47.

She arrived at Brackenridge at 4:39, wants to leave around 5:39. The bus at Brackenridge at 5:40 is 1 minute after 5:39 (5:40 - 5:39 = 1 minute), which is close. The previous bus was at 5:20 (5:39 - 5:20 = 19 minutes), so 5:40 is closer.

Step3: Find arrival time at East Liberty

Now, the bus departs Brackenridge at 5:40 (from "To Downtown Pittsburgh" schedule, Brackenridge column, row with 5:40). Now, we need to find the arrival time at East Liberty (East Liberty Stop D) from the "To Downtown Pittsburgh" schedule. The "To Downtown Pittsburgh" schedule has East Liberty (East Liberty Station D) at 6:15, 6:35, 6:55, 7:10, 7:25, 7:40, 7:55, 8:15, 8:41. Wait, no, let's check the columns. The "To Downtown Pittsburgh" schedule: the stops are Harrison, Bakertown Rd, Harrison, Freeport Rd, etc., then East Liberty Station D. Let's find the row with Brackenridge at 5:40. The row with Brackenridge at 5:40: let's see, the first row is 5:08 (Harrison), 5:11 (Freeport Rd), 5:18 (Natrona Heights), 5:20 (Brackenridge), 5:28 (Tarentum), 5:32 (Creighton), 5:42 (Springdale), 5:44 (Cheswick), 5:50 (Harmar), 6:01 (RIDC), 6:12 (Larimer), 6:15 (East Liberty). Wait, no, the times: 5:20 at Brackenridge, 5:28 at Tarentum, 5:32 at Creighton, 5:42 at Springdale, 5:44 at Cheswick, 5:50 at Harmar, 6:01 at RIDC, 6:12 at Larimer, 6:15 at East Liberty.

Second row: 5:28 (Harrison), 5:31 (Freeport Rd), 5:38 (Natrona Heights), 5:40 (Brackenridge), 5:48 (Tarentum), 5:52 (Creighton), 6:02 (Springdale), 6:04 (Cheswick), 6:10 (Harmar), 6:21 (RIDC), 6:32 (Larimer), 6:35 (East Liberty). Ah, there we go. So the row with Brackenridge at 5:40: the East Liberty column (East Liberty Station D) is 6:35? Wait, no, let's list the columns in "To Downtown Pittsburgh":

Columns (from left to right): Harrison, Bakertown Rd, Harrison, Freeport Rd (opp Oak Manor Dr), Natrona Heights, Freeport Rd (at Alabama Ave), Brackenridge (Ninth Penn Ave past), Tarentum (4th Ave), Harmar (Alpha Dr), RIDC (Rt 28 Expwy Ramp), Larimer, Washington Blvd (at Frankstown Ave), East Liberty Station D.

So the row with Brackenridge at 5:40: let's check the times. The row is:

Harrison: 5:28

Bakertown Rd: (next column) 5:31

Harrison: (next) 5:31? Wait, no, the first column is Harrison (5:08, 5:28, 5:48, 6:03, 6:14, 6:29, 6:44, 7:04, 7:34)

Second column: Bakertown Rd (5:11, 5:31, 5:51, 6:06, 6:17, 6:32, 6:47, 7:07, 7:37)

Third column: Harrison (5:11, 5:31, 5:51, 6:06, 6:17, 6:32, 6:47, 7:07, 7:37) – no, maybe I'm misreading. Wait, the "To Downtown Pittsburgh" schedule: the first row (top row) is 5:08 (Harrison), 5:11 (Freeport Rd opp Oak Manor Dr), 5:18 (Natrona Heights), 5:20 (Brackenridge), 5:28 (Tarentum), 5:32 (Creighton), 5:42 (Springdale), 5:44 (Cheswick), 5:50 (Harmar), 6:01 (RIDC), 6:12 (Larimer), 6:15 (East Liberty).

Second row: 5:28 (Harrison), 5:31 (Freeport Rd), 5:38 (Natrona Heights), 5:40 (Brackenridge), 5:48 (Tarentum), 5:52 (Creighton), 6:02 (Springdale), 6:04 (Cheswick), 6:10 (Harmar), 6:21 (RIDC), 6:32 (Larimer), 6:35 (East Liberty). Yes, so Brackenridge at 5:40, East Liberty at 6:35.

Wait, but let's confirm the direction. The "To Downtown Pittsburgh" schedule is going from Harrison (outer) to Downtown, so East Liberty is a stop before Downtown. So the bus departs Brackenridge at 5:40, arrives at East Liberty at 6:35.

Wait, but let's check the time difference. She departs Brackenridge at 5:40, which is 1 minute after 5:39 (the 1-hour mark). The arrival at East Liberty is 6:35.

Wait, but let's re-examine the first part. Maybe I mixed up the directions. Let's start over.

Marcy wants to go from East Liberty (East Liberty bus stop) to Brackenridge (store), then back to East Liberty.

First, find the bus from East Liberty to Brackenridge. The "To Tarentum - Natrona Heights" schedule is the direction from Downtown to Tarentum, so East Liberty is a stop on that route. The departure from East Liberty (East Liberty Stop B) is 3:45, and the arrival at Brackenridge (Ninth Penn Ave) is 4:39 (as per the schedule: 3:45 at East Liberty, 4:39 at Brackenridge).

Now, she wants to return, so she needs the bus from Brackenridge to East Liberty, which is the "To Downtown Pittsburgh" schedule (since that's the direction from Tarentum/Harrison to Downtown, passing East Liberty).

So in the "To Downtown Pittsburgh" schedule, we need to find the bus that departs Brackenridge as close to 4:39 + 1 hour = 5:39 as possible.

Looking at the "To Downtown Pittsburgh" schedule, the Brackenridge (Ninth Penn Ave past) column has times:

- 5:20 (first row)

- 5:40 (second row)

- 6:00 (third row)

- 6:15 (fourth row)

- 6:27 (fifth row)

- 6:42 (sixth row)

- 6:57 (seventh row)

- 7:17 (eighth row)

- 7:47 (ninth row)

The time 5:39 is between 5:20 and 5:40. 5:40 is 1 minute after 5:39, which is closer than 5:20 (19 minutes before). So she takes the bus that departs Brackenridge at 5:40.

Now, find the arrival time at East Liberty (East Liberty Station D) from the "To Downtown Pittsburgh" schedule, same row as Brackenridge at 5:40.

Looking at the "To Downtown Pittsburgh" schedule, the row with Brackenridge at 5:40:

- Brackenridge: 5:40

- Next stops: Tarentum (5:48), Harmar (6:10)? Wait, no, the columns are in order: Harrison, Freeport Rd opp Oak Manor Dr, Natrona Heights, Freeport Rd at Alabama Ave, Brackenridge, Tarentum, Harmar, RIDC, Larimer, Washington Blvd, East Liberty, Downtown.

Wait, the second row of "To Downtown Pittsburgh" (times: 5:28, 5:31, 5:38, 5:40, 5:48, 5:52, 6:02, 6:04, 6:10, 6:21, 6:32, 6:35, 6:21, 6:28). Wait, the East Liberty column (East Liberty Station D) in that row is 6:35. So the bus departs Brackenridge at 5:40, arrives at East Liberty at 6:35.

Let's verify the time from Brackenridge to East Liberty. The bus departs Brackenridge at 5:40, arrives at East Liberty at 6:35. The duration is 55 minutes, which is reasonable.

Alternatively, maybe the first direction was wrong. Let's check the "To Downtown Pittsburgh" schedule for East Liberty's departure times. The "To Downtown Pittsburgh" schedule has East Liberty (East Liberty Station D) at 6:15, 6:35, 6:55, 7:10, 7:25, 7:40, 7:55, 8:15, 8:41. So those are arrivals at East Liberty from the outer areas. So to go from East Liberty to Brackenridge, she needs the bus going outward (to Tarentum), which is the "To Tarentum - Natrona Heights" schedule. So departure from East Liberty (East Liberty Stop B) at 3:45, arrival at Brackenridge at 4:39. Then, to return, she needs the bus going inward (to Downtown), which is the "To Downtown Pittsburgh" schedule, departing Brackenridge at 5:40 (closest to 5:39), arriving at East Liberty at 6:35.

Yes, that makes sense. So the arrival time back at East Liberty is 6:35.

Answer:

6:35 (or 6:35 PM)