Ziptrac commuter trains carry passengers between the three cities of A

The solution is Ziptrack 9.30 am and local bus 10.00 am but I don't know how to solve it.

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.

Posted from my mobile device

The bit in Red is not possible. The express train, as mentioned in the question, does not stop at D. The answer, from my calculations, is 10 am for the train and 10:30 am for the bus, leading to an arrival difference of about 50 mins.

train does not leave 10am and 11 am as the train only leaves on the half hour

" Trains leave Amra promptly on the half hour beginning at 8 am"; this, to me, means every half hour rather than at 8:30, 9:30, 10:30 etc.

if that's the case, then it would have been written like "the train leaves every half hour starting 8am"
comparing this to the bus statement "the bus leaves promptly every half hour starting at 9:30am"

THE half hour, then that means it's the definite noun....only THE half hour of every hour beginning 8am....

LOL i was stumped by this statement too.
At first I was shocked by the sheer math required for every scenario but it's really the case that both train and bus leaves every half hour because there are too many possibilities and the answer choices might not be unique.

Then I re-read the question. The presence of " on the half hour" makes the question a lot more simpler and less math is required.
You can use logic to rule out some choices for the train.

but again this is not from OG.... the prep providers have a way of spinning the question in the weirdest way.

GMATNinja, any thoughts on this question? thanks

Hi Bunuel, VeritasKarishma and other Quant experts,
Please provide a solution to this tricky question.
Thanks

Bus travels at 3/4th speed of train while train travels 10 mph faster. So the difference of 1 on ratio scale is actually 10.
Speed of Bus = 30 mph, Time taken by bus from A to D (10 miles) = 20 mins
Speed of train = 40 mph, Time taken by train from A to D (10 miles) = 15 mins and 10 mins layover so it starts from D in 25 mins.
It reaches G in another 50 mins i.e. in total 75 mins (1 hr 15 mins)

This is how the trains and buses will run (though you don't need to do all these calculations in the exam)

Train starts from A at 8, starts from D at 8:25 and reaches G by 9:15.
Train starts from A at 8:30, starts from D at 8:55 and reaches G by 9:45.
Train starts from A at 9 and reaches G by 10.
Train starts from A at 9:30, starts from D at 9:55 and reaches G by 10:45.
Train starts from A at 10, starts from D at 10:25 and reaches G by 11:15.
Train starts from A at 10:30 and reached G by 11:30.
Train starts from A at 11, starts from D at 11:25 and reaches G by 12:15.
Trains starts from A at 11:30, starts from D at 11:55 and reaches G by 12:45.


Bus goes from A to D in 20 mins
Bus starts from A at 9:30 and reaches D at 9:50.
Bus starts from A at 10 and reaches D at 10:20.
Bus starts from A at 10:30 and reaches D at 10:50.
Bus starts from A at 11 and reaches D at 11:20.
Bus starts from A at 11:30 and reaches D at 11:50.
Bus starts from A at 12 and reaches D at 12:20.


The first person should catch one of the slow trains. The second person should catch the next bus. So the difference in their time of catching train/bus will be 30 mins.
Also, the first person should catch a train of 9 am or later because buses start by 9:30. But at 9 am, we have the express so he should take the 9:30 am train. So the second person will take the 10 am bus.
There will be a half an hour gap between them when they reach G.

Checking for rest of the options:
If the first person takes the train at 10, the second person takes the bus at 10:30 but there is no train from D till 11:25. So he loses time.
Train from A at 10:30 is an express and train from A at 11 cannot be taken because then second person will need to take the bus at 11:30 (not there in options)

The ONLY calculations required are for train at 9:30 and train at 10:00.

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