Train A leaves New York at 9am Eastern Time on Monday

Question

Train A leaves New York at 9am Eastern Time on Monday, headed for Los Angeles at a constant rate of 40 miles per hour. On the same 3,000-mile stretch of track, Train B leaves Los Angeles at noon Eastern Time on Monday, traveling to New York at its constant rate of 60 miles per hour, with one exception: Train B is delayed for exactly 2 hours in Las Vegas (approximately 200 miles from Los Angeles) due to track maintenance. Assuming the time it takes for Train B to decelerate and re-accelerate when stopping and resuming in Las Vegas is negligible, at what time (Eastern Time) will the two trains meet?

A) 3:00pm on Tuesday
B) 4:30pm on Tuesday
C) 5:00pm on Tuesday
D) 6:00pm on Tuesday
E) 7:30pm on Tuesday

A) 3:00pm on Tuesday
B) 4:30pm on Tuesday
C) 5:00pm on Tuesday
D) 6:00pm on Tuesday
E) 7:30pm on Tuesday

Bunuel · Accepted Answer

We can assume that B leaves Los Angeles not at noon but at 2pm Eastern Time, so 5 hours later than A leaves New York.

In 5 hours A covers 5*40=200 miles. So, A and B together should cover 3,000-200=2,800 miles.

Combined rate = 40 + 60 = 100 miles per hour.

To cover 2,800 miles they'll need 2,800/100=28 hours.

2pm Eastern Time on Monday + 28 hours = 6pm Eastern Time on Tuesday.

Answer: D.

SVaidyaraman · Answer

When the trains travel towards each other, we have to consider the combined speed but only when one of them travel we have to consider only that train's speed.

1. Here, for the first 3 hours i.e., between 9 am and 12 noon only train A travels. The distance covered by it is 3*40 = 120 miles. The remaining distance is 3000-120=2880 miles

2. Also after that for exactly 2 hours train A only travels because train B stops at Las Vegas for 2 hours. The distance covered by train A during this period is 2*40=80 miles. Remaining distance is 2880-80=2800 miles

3. The distance of 2800 miles is covered with both trains moving towards each other. Therefore for this distance combined speed is to be taken. Time taken to cover 2800 miles = 2800/(60+40) = 28 hours.

4. Train A traveled for 5 hours alone and for 28 hours together with train B. The total hours traveled by A is 33 hours. Since it started at 9 am on Monday the two trains will meet 33 hours later i.e., 6 pm on Tuesday.

WholeLottaLove · Answer

Train A leaves New York at 9am Eastern Time on Monday, headed for Los Angeles at a constant rate of 40 miles per hour. On the same 3,000-mile stretch of track, Train B leaves Los Angeles at noon Eastern Time on Monday, traveling to New York at its constant rate of 60 miles per hour, with one exception: Train B is delayed for exactly 2 hours in Las Vegas (approximately 200 miles from Los Angeles) due to track maintenance. Assuming the time it takes for Train B to decelerate and re-accelerate when stopping and resuming in Las Vegas is negligible, at what time (Eastern Time) will the two trains meet?

A) 3:00pm on Tuesday
B) 4:30pm on Tuesday
C) 5:00pm on Tuesday
D) 6:00pm on Tuesday
E) 7:30pm on Tuesday

I think I am being thrown off by Train A starting before train B. How do I figure out how long it takes for them to meet one another if one train starts off before the other?

VictoryVictoria · Answer

To benefit the GMATClub community, please avoid the same mistake that I did. Took way too long to graph the journey, got thrown off scent by the whole Train B delayed in Vegas thing.

Action item: I think Bunuel's solution is the most actionable for me given exam situation.

I need to retrain my brain to stop relying so much on graphing the questions because it is hurting my GMAT score and not helping at all. This has happened several times, so I suspect I just need to train my brain to framework this type of Problem to Bunuel's template and just get on with the math. Next step is for me to try, embed this to muscle memory, see if there is any improvement in timing & accuracy.

effatara · Answer

Took another look at the problem and found a simpler and faster solution:
Let's say Train A (TA) travels for 't' hrs after its departure from NY up to the point it meets Train B (TB). Thus, TB travels for (t -5)hrs since it started 3 hrs after TA and lost an additional 2 hrs at Vegas. So TA and TB travel t*40 miles and (t-5)*60 miles respectively to cover the 3000 miles between NY and LA.
So, 40*t +60*(t-5) = 3000 ----> t = 33 hrs. Since TA started at 9:00 am Monday, the two trains will meet at 6:00 pm Tuesday.

KarishmaB · Answer

There are various ways to do this problem.

Method 1:  
We need to find at what time they meet. Say they meet t hrs after train A starts at 9 AM EST. 
Train A runs for t hrs. Train B runs for (t - 5) hrs since it starts 3 hrs late and takes a break of 2 hrs in between (It doesn't matter whether the break was taken 10 mins into the journey, 1 hr or 2 hrs as long as it was early enough so that the break was over before they met).
Together they covered 3000 miles.

40 * t + 60*(t - 5) = 3000
t = 33 hrs
That gives us 6 pm Tuesday.

Method 2: Explanation of Bunuel's method above that you (@teenavijay) are referring to

It doesn't matter WHERE the break was taken as long as it was early enough. For the rest of time, train B ran at the steady speed of 60 mph. So let's assume that the break was taken at the starting point itself such that train B started 5 hrs after train A. Think about it logically:
I start from home towards your home at 9 AM and walk consistently. 
In one case, you start from your home at 12 noon, walk for 5 mins, then rest for 2 hrs and then walk consistently towards me. We meet at 6 PM.
In another case, you start from your home at 12 noon, walk for 10 mins, then rest for 2 hrs and then walk consistently towards me. 
In yet another case, you start from your home at 12 noon, walk for 1 hr, then rest for 2 hrs and then walk consistently towards me.
Are the cases different? No. What part of the journey you covered at what time is irrelevant. You covered that distance at your consistent speed.

Hence, we can shift the break to the starting point and solve from there.

Now the question becomes:
Train A leaves New York at 9am Eastern Time on Monday, headed for Los Angeles at a constant rate of 40 miles per hour. On the same 3,000-mile stretch of track, Train B leaves Los Angeles at 2 PM Eastern Time on Monday, traveling to New York at its constant rate of 60 miles per hour. At what time (Eastern Time) will the two trains meet?

From 9 AM to 2 PM, in 5 hrs, train A travels 5 * 40 = 200 miles.

So total distance they need to travel from 2 PM onwards is 3000 - 200 = 2800 miles

Time taken = 2800/(40 + 60) = 28 hrs

28 hrs after 2 PM Monday again gives us 6 PM Tuesday.

Method 3: We can map their journey.

Train A simply travels at 40 mph starting at 9 AM. 
Train B starts at 12 noon at 60 mph and travels 200 miles. It reaches Vegas after 200/60 = 20/6 hrs. 
It waits there for 2 hrs so after 20/6 + 2 = 16/3 hrs, both trains travel interrupted towards each other. 
In these (3+16/3) hrs, train A covered (3 + 16/3)*40 = 120 + 640/3 miles.
So after (3+16/3) hrs, distance between them is 3000 - 200 - 120 - 640/3 = 2680 - 640/3 miles

Time taken = Distance between them/Relative speed = (2680 - 640/3) / (40 + 60) = (268/10 - 64/30) hrs
Hence total time taken = 3 + 16/3 + (268/10 - 64/30) hrs = 33 hrs

That gives us 6 pm Tuesday.

Hope you see that the intent of this question is to make you realise that the time of break is irrelevant as long as it is early enough. Method 3 is a nightmare.

avaniguptaonly · Answer

hi  Bunuel

why you assumed 5 hrs later

Bunuel · Answer

Train A left New York at 9am Eastern Time on Monday.

Train B left Los Angeles at noon Eastern Time on Monday. But it was delayed for 2 hours in Las Vegas. So, I adjusted the effective starting time of Train B by adding those 2 hours of delay to its starting time. This way, instead of doing calculations with the delay in between, it becomes a straightforward problem.

So:
9am (when Train A left) to noon (when Train B originally left) = 3 hours
Adding the 2-hour delay of Train B = 3 + 2 = 5 hours

Thus, effectively, you can consider that Train B started 5 hours after Train A. This approach simplifies the problem considerably.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Train A leaves New York at 9am Eastern Time on Monday

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Train A leaves New York at 9am Eastern Time on Monday

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards