Starting at 5.00 am, every half hour there is flight from San Francisco airport

Question

Starting at 5.00 am, every half hour there is flight from San Francisco airport to Los Angles International airport. Suppose that none of these planes is completely sold out and they have always room for passengers. A person who wants to fly to L.A arrives at a random time between 8.45 am and 9.45 am. What is the average time this person needs to wait? Starting at 5.00 am, every half hour there is flight from San Francisco airport to Los Angles International airport. Suppose that none of these planes is completely sold out and they have always room for passengers. A person who wants to fly to L.A arrives at a random time between 8.45 am and 9.45 am. What is the average time this person needs to wait?

Explanation / Answer

Note:- Calculations have been made on the basis of minute as a unit of time

The flights start at 5:00 AM and operates at a gap of 30 Minutes thereon

In this manner the next flights are scheduled to be at :- 5:30 , 6:00, 6:30, 7:00, 7:30, 8:00, 8:30, 9:00,9:30, 10:00 and so on

A person who wants to fly to LA arriving at a random time between 8:45 and 9:45

shall have the flights at 9:00 , 9:30 and 10:00 in his range depending upon the time of his arrival

For example if he arrives at precisely 8:45 he will have to wait till 9:00 or 15 minutes

if he arrives at anytime after 9:00 he will have to wait till 9:30 or 30 minutes

and if he arrives after 9:30 he will have to wait till 10:00 or 30 minutes

The person has an equal probability of arriving at any time between time duration 8:45 to 9:45

The Person will have to weight for an average of 15:45 hrs / 61 = 15 minutes

Arrival Time Waiting Time 08:45 00:15 08:46 00:14 08:47 00:13 08:48 00:12 08:49 00:11 08:50 00:10 08:51 00:09 08:52 00:08 08:53 00:07 08:54 00:06 08:55 00:05 08:56 00:04 08:57 00:03 08:58 00:02 08:59 00:01 Flight Deprt 09:00 0:30:00 09:01 00:29 09:02 00:28 09:03 00:27 09:04 00:26 09:05 00:25 09:06 00:24 09:07 00:23 09:08 00:22 09:09 00:21 09:10 00:20 09:11 00:19 09:12 00:18 09:13 00:17 09:14 00:16 09:15 00:15 09:16 00:14 09:17 00:13 09:18 00:12 09:19 00:11 09:20 00:10 09:21 00:09 09:22 00:08 09:23 00:07 09:24 00:06 09:25 00:05 09:26 00:04 09:27 00:03 09:28 00:02 09:29 00:01 Flight Deprt 09:30 00:30 09:31 00:29 09:32 00:28 09:33 00:27 09:34 00:26 09:35 00:25 09:36 00:24 09:37 00:23 09:38 00:22 09:39 00:21 09:40 00:20 09:41 00:19 09:42 00:18 09:43 00:17 09:44 00:16 09:45 00:15 61 15:45

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