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22 Jul 2026, 12:38
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
32% (03:30) correct
68%
(02:30)
wrong
based on 25
sessions
History
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Time
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Not Attempted Yet
The subway from Peterson Station departs on the hour and at quarter-hour intervals. Bernie’s 5:40 A.M. train was due to arrive at Peterson Station at 9:00 A.M. after traveling at its usual speed of 120 miles per hour. The train arrived at the halfway point on time but then completed the second half at a speed that varied between 30 and 80 miles per hour. If Bernie took the first subway that departed at least 40 minutes after her train arrived at Peterson Station, at how many different times could her subway have departed?
(A) 13
(B) 14
(C) 15
(D) 16
(E) 17
(A) 13
(B) 14
(C) 15
(D) 16
(E) 17
23 Jul 2026, 02:06
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General expected journey of the train:
- Speed = 120 miles/hour = 2 miles/min.
- Time taken = Time lapsed from (5:40 AM to 9:00 AM) = 3 hours 20 min = 200 min.
- Hence, distance covered by the train = 200 / (1/2) = 400 miles.
Journey - First Half:
- Speed = 2 miles/min.
- Distance = 200 miles (halfway point).
- Hence, time taken = 200/2 = 100 minutes
- Time at which the train reached the halfway point = 100 minutes from 5:40 AM = 7:20 AM.
Journey - Second Half:
- Distance = 200 miles.
- Speed -> varied from 30 miles/hour to 80 miles/hour. i.e. between 1/2 miles/min to 4/3 miles/min.
- If the entire 200-mile distance was covered at 1/2 miles/min, then, the time taken would have been 200 / (1/2) = 400 min.
- If the entire 200-mile distance was covered at 4/3 miles/min, then, the time taken would have been 200 / (4/3) = 150 min.
In reality, the speed varied between these points. The actual average speed would be something greater than 1/2 miles/min and something lesser than 4/3 miles/min.
So,
The actual time taken for the second half of the journey would be between 150 min and 400 min.
150 min < time taken for second half < 400 min.
So, by when would the train arrive at Peterson Station?
>150 min from 7:20 AM and <400 min from 7:20 AM.
i.e.,
9:50 AM < arrival time < 14:00 PM
Bernie waited at least 40 min after arrival, before getting on the subway.
So,
- Bernie could have got on a subway after 10:30 AM. The first possible subway taken is 10:45 AM.
- Bernie reached the station max by 13:59:59 PM. So, 40 min from this point is 14:39:59 PM. So, the first possible subway taken in this case is 14:45 PM.
How many different times could her subway have departed?
10:45, 11:00,.....14:45 -> 17. Choice E.
---
Harsha
- Speed = 120 miles/hour = 2 miles/min.
- Time taken = Time lapsed from (5:40 AM to 9:00 AM) = 3 hours 20 min = 200 min.
- Hence, distance covered by the train = 200 / (1/2) = 400 miles.
Journey - First Half:
- Speed = 2 miles/min.
- Distance = 200 miles (halfway point).
- Hence, time taken = 200/2 = 100 minutes
- Time at which the train reached the halfway point = 100 minutes from 5:40 AM = 7:20 AM.
Journey - Second Half:
- Distance = 200 miles.
- Speed -> varied from 30 miles/hour to 80 miles/hour. i.e. between 1/2 miles/min to 4/3 miles/min.
- If the entire 200-mile distance was covered at 1/2 miles/min, then, the time taken would have been 200 / (1/2) = 400 min.
- If the entire 200-mile distance was covered at 4/3 miles/min, then, the time taken would have been 200 / (4/3) = 150 min.
In reality, the speed varied between these points. The actual average speed would be something greater than 1/2 miles/min and something lesser than 4/3 miles/min.
So,
The actual time taken for the second half of the journey would be between 150 min and 400 min.
150 min < time taken for second half < 400 min.
So, by when would the train arrive at Peterson Station?
>150 min from 7:20 AM and <400 min from 7:20 AM.
i.e.,
9:50 AM < arrival time < 14:00 PM
Bernie waited at least 40 min after arrival, before getting on the subway.
So,
- Bernie could have got on a subway after 10:30 AM. The first possible subway taken is 10:45 AM.
- Bernie reached the station max by 13:59:59 PM. So, 40 min from this point is 14:39:59 PM. So, the first possible subway taken in this case is 14:45 PM.
How many different times could her subway have departed?
10:45, 11:00,.....14:45 -> 17. Choice E.
---
Harsha
