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Ziptrac commuter trains carry passengers between the three cities of A

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Ziptrac commuter trains carry passengers between the three cities of A  [#permalink]

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New post Updated on: 15 Nov 2019, 08:08
Project IR Butler 2019-20 - Get one IR Question Everyday
Question # 46, Date : 15-Nov-2019
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Ziptrac commuter trains carry passengers between the three cities of Amra, Delta, and Gabrin. Trains leave Amra promptly on the half hour beginning at 8 am, and travel 10 miles to Delta. After a 10 minute stopover the trains then travel for 50 minutes to Gabrin. However, every third train originating from Amra is a one-hour express to Gabrin that does not stop at Delta. From the Amra station, commuters can also take a local bus, which leaves promptly every half hour starting at 9:30 am, to the Delta station. The local bus travels 3/4 as fast as the train, while the train travels 10 miles per hour faster than the bus does.

Use the buttons below to indicate the departure times for a Ziptrac train and a local bus that would produce the shortest difference in arrival times at Gabrin for two passengers, one of whom promptly catches the Ziptrac train at Amra, and one of whom is too late to catch the same Ziptrac train at Amra, and so takes the next local bus to Delta, and then the next available train to Gabrin.

ZiptrackLocal BusValues
8.30 am
9.30 am
10 am
10.30 am
11 am

Originally posted by MartyKaan on 14 Nov 2019, 10:03.
Last edited by SajjadAhmad on 15 Nov 2019, 08:08, edited 2 times in total.
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Re: Ziptrac commuter trains carry passengers between the three cities of A  [#permalink]

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New post 14 Nov 2019, 10:56
10:30 am for Ziptrack & 10:00 am for local bus ?

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Re: Ziptrac commuter trains carry passengers between the three cities of A  [#permalink]

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New post 15 Nov 2019, 10:08
The solution is Ziptrack 9.30 am and local bus 10.00 am but I don't know how to solve it.
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Re: Ziptrac commuter trains carry passengers between the three cities of A  [#permalink]

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New post 15 Nov 2019, 12:04
2
Hey I got it, actually I wrongly wrote the answer for Ziptrack as 10:30, as it should be 9:30 am for Ziptrack and 10:00 am for bus

So let me explain here :

From Amra(A) to Delta(D) the distance covered by the train is 10 miles and from D to G(Gabrin) the time taken is 50 min with a 10 min stop at D. And we know that the train starts at 8 am and runs every hour hour, so they run at 8,8:30,9.....
Now every third train that is trains running at 9,10:30,12 are express trains, which take 1 hour to complete the journey.

Now per the question the speed of the bus = .75 Speed of train

And speed of train = speed of bus + 10
So speed of train = 40 miles/hour
Speed of bus = 30 miles/hour

So from A to D the train takes 15 minutes

And bus takes 10 miles/30 miles/hr = 20 minutes from A to D
And bus starts at 9:30 and runs every half hour

So our aim here should be such that the guy taking a bus should board bus at such a time that he can get the Express train quickly and other person takes the usual train so that the travel time difference between both of them is minimized

So if we go by the options for Local bus 8:30 am is not possible, and if I take 9:30 for bus then the person will reach to D at 9:50 and then he has to wait for 40 mins for express train, because if he takes the norm train at 10:00 am then it will again increase the time difference, so the bus should be taken at 10:00 am so that the person can reach to D in 20 minutes and then wait for 10 mins and take the express train at 10:30 am, reaching G at 11:30 am

Now the Ziptrack should be taken at 9:30 am so that the total journey can be completed in 15 minutes (from A- D)+10 mins (stopover)+50 mins(D -G), so these train will reach at 10:45 am.

So the time difference between both would be 45 minutes.

Now if you check with other possibilities the time would be around 50/55 minutes.

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Re: Ziptrac commuter trains carry passengers between the three cities of A   [#permalink] 15 Nov 2019, 12:04
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