Train A Leaves New York at 9am Eastern Time on Monday, Headed for Los Angeles at a Constant Rate GMAT Problem Solving

Question: Train A leaves New York at 9 am 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?

1. 3:00pm on Tuesday
2. 4:30pm on Tuesday
3. 5:00pm on Tuesday
4. 6:00pm on Tuesday
5. 7:30pm on Tuesday

‘Train A leaves New York at 9am Eastern Time on Monday, headed for Los Angeles at a constant rate of 40 miles per hour' - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “The Official Guide for GMAT Reviews”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:

Approach Solution 1:
It is given in the question that trains A leaves New York at 9 am 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. We can assume that the time it takes for Train B to decelerate and re-accelerate when stopping and resuming in Las Vegas is negligible, it is asked at what time (Eastern Time) will the two trains meet?
It can be assumed that B leaves Los Angeles not at noon but at 2 PM Eastern Time, so 5 hours later than A leaves New York.
In 5 hours A will cover 5 * 40 = 200 miles. So A and B together cover 3000 -200 = 2800 miles
Combined rate of their speed = 40 + 60 = 100 miles per hour
To cover 2,800 miles they’ll need 2800/100 hours = 28 hours.
2 PM eastern time on Monday + 28 hours = 6 PM Eastern time on Tuesday
Therefore the correct answer will be option D

Correct Answer: D

Approach Solution 2:
When the trains travel towards each other, we have to take into account the relative speed but when only one train is traveling we have to consider only that train's speed.
Here,
for the first 3 hours of the journey,
between 9 am and 12 noon only trains A travel.
The distance covered by it is 3*40 = 120 miles.
The remaining distance is 3000-120=2880 miles
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.
The remaining distance is 2880-80=2800 miles
The distance of 2800 miles is covered with both trains moving towards each other. Therefore for this distance relative speed has to be taken.
Time taken to cover 2800 miles = 2800/ (60+40) = 28 hours.
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.

Correct Answer: D

Approach Solution 3:

It is given in the problem that Train A travels at 40 mph starting at 9 AM.
So, Train B starts at 12 noon at 60 mph and travels 200 miles. The trains reach Vegas after 200/60 = 20/6 hrs.
Therefore it waits for 2 hrs.
So after 20/6 + 2 = 16/3 hrs, both trains travel interrupted towards each other.
So for (3+16/3) hrs, train A covered (3 + 16/3)*40 = 120 + 640/3 miles.
So after (3+16/3) hrs, the distance between the two trains is 3000 - 200 - 120 - 640/3 = 2680 - 640/3 miles
So, the 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.

Correct Answer: D

Suggested GMAT Problem Solving Questions

• A Man has 1044 Candles. After Burning, He can Make a New Candle GMAT Problem Solving
• An Equilateral Triangle ABC is Inscribed in Square ADEF GMAT Problem Solving
• A Popular Website Requires Users to Create a Password Consisting of Digits Only GMAT Problem Solving
• A Furniture Store Sells Only Two Models of Desks, Model A and Model B GMAT Problem Solving
• In a Drawer, There are 4 White Socks, 3 Blue Socks, and 5 Grey Socks GMAT Problem Solving
• There are 100 Apples in a Bag of which 98% are Green and Rest are Red GMAT Problem Solving
• A palindrome is a number that reads the same forward and backward GMAT Problem Solving
• Three Cars Leave From A To B In Equal Time Intervals GMAT Problem Solving
• An Inlet Pipe can Fill in an Empty Cistern in 30 minutes GMAT Problem Solving
• Iqbal Dealt Some Cards to Mushtaq and himself from a Full Pack of Playing Cards GMAT Problem Solving
• A Zookeeper Counted the Heads of the Animals in a Zoo and Found it to be 80 GMAT Problem Solving
• A Shop Stores x kg of Rice. The First Customer Buys half this Amount Plus half a kg of Rice GMAT Problem Solving
• In a Class of 120 Students Numbered 1 to 120, All Even Numbered Students Opt for Physics GMAT Problem Solving
• Machine A Produces bolts at a Uniform Rate of 120 Every 40 seconds GMAT Problem Solving
• Out of 7 Consonants and 4 Vowels, How Many Words of 3 Consonants and 2 Vowels Can be Formed? GMAT Problem Solving
• 4 Bells Toll Together at 9:00 A.M. They Toll After 7, 8, 11 and 12 Seconds GMAT Problem Solving
• 12 Marbles are Selected at Random from a Large Collection of White, Red, Green and Yellow Marbles GMAT Problem Solving
• Find the greatest number that will divide 43, 91 and 183 GMAT Problem Solving
• Of the 150 Houses in a Certain Development GMAT Problem Solving
• A man can hit a target once in 4 shots. If he fires 4 shots in succession GMAT Problem Solving