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[sfbay]

Train A leaves New York for Boston at 3 PM and travels at the constant speed of 100 mph. An hour later, it passes Train B, which is making the trip from Boston to New York at a constant speed. If Train B left Boston at 3:50 PM and if the combined travel time of the two trains is 2 hours, what time did Train B arrive in New York?


(1) Train B arrived in New York before Train A arrived in Boston.
(2) The distance between New York and Boston is greater than 140 miles.


It is MGMAT question and has been posted before but i did not see a solution.

[RonPurewal]

that's the "challenge problem archive" question from 10/21/02 -- if you have access to our site, then you can look up the solution there.

like other "challenge problem archive" problems, this one is WAY WAY harder than just about anything you'd ever see on the gmat, so i wouldn't sweat too hard if i were you. better to concentrate on the problems that are decently representative of what you'll actually see, and to view the challenge archive as, more or less, a nerdy form of recreation.

[sudhir.18n]

Train A leaves New York for Boston at 3 PM and travels at the constant speed of 100 mph. An hour later, it passes Train B, which is making the trip from Boston to New York at a constant speed. If Train B left Boston at 3:50 PM and if the combined travel time of the two trains is 2 hours, what time did Train B arrive in New York?


(1) Train B arrived in New York before Train A arrived in Boston.
(2) The distance between New York and Boston is greater than 140 miles.


It is MGMAT question and has been posted before but i did not see a solution.

I think the answer is D . Took 10 mints to solve this .. not sure if this is the quickest way to do . Ron need ur help ..


Train A Train B

Rate 100 mph r
Time 2 - t t
Distance d d

2 equation from this ;
A. 100(2-t) =d
B. rt=d

Substituting B in A we get

100(2-t) = rt; solve for t

200-100t = rt
200= t(r+100)
t= 200/(r+100)...........................C

We also know that train A is traveling @ 100mph .. An hour later,
hence in 1 hr train A travelled 100 miles
Train B started 50 mints late , hence in 10 mints it wud have travelled r/6 miles.

Thus total distance ; d= 100+r/6.......................D
From equation B we know d=rt; substitute D in B we get
rt= 100+r/6.....................E

Now substitute C in E
r(200/(r+100))= 100+r/6, solve for r we get
(r - 300) (r - 200) = 0

Hehnce we know train B is travelling wither at 300mph or 200 mph.

Assuming it travels at 200 mph.
train A has travelled 100 miles , train B will travel 200/6= 33.33 mph
Hence the total distance is 100+33.33 = 133.33 mph.

Option 2 says the distance is >140 mph. Thus we can eliminate ACE. left with BD

assuming train B travels at 300 mph,
train A 100, Train B 300/6 = 50
total distance 150 mph. Hence train B will take 1/2 hr and train A will 1.5 hrs.
Thus, train A will trach at 4'30 pm and train B at 4'20 pm. satisfies option 1 as well.

Hence both independently can answer,hence D

[jnelson0612]

D is indeed the answer! Very impressive that you could solve, as this problem is much harder than anything you will see on the GMAT.

[Ace1]

D is indeed the answer! Very impressive that you could solve, as this problem is much harder than anything you will see on the GMAT.

Hi,
I tried solving this problem with the below formula, which covers the concept of combination of speed when 2 objects are travelling towards each other. Total distance travelled till they met / Sum of speeds = Total time travelled till they met
This should give the combination of time over a set distance.

Let x be the distance travelled by B till it met A
So,
100 + x / 100 + 6x = 7/6 (1hr 10 mins)
Now, 6(100 + x) = 7(100 + 6x) >> This doesnt give the desired outcome.. Can you tell me where did i go wrong with the above formula?

The idea was to find a suitable value for x and then fit it alongwith the information provided.

Please assist.

[RonPurewal]

^^ i don't think you can do what you're trying to do, because the two trains don't travel for the same amount of time. (one of them starts at 15:00, the other at 15:50.)

[RonPurewal]

also, not quite sure where the expression (100 + x)/(100 + 6x) comes from... perhaps you can post a quick derivation of that. thanks.