Lesson: Multiple Trips or Multiple Travelers

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Two trains, X and Y, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; Train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had Train X traveled when it met Train Y?

(A) 37.5
(B) 40.0
(C) 60.0
(D) 62.5
(E) 77.5 Don't know what should be done after taking out per hour speed of x and y
gmat-admin's picture

There are some very nice solutions here: http://www.beatthegmat.com/trains-from-two-opposite-ends-t286355.html

Please let me know if you need any clarification.

Speed of Train X 20kmph and Train Y 100/3 kmph.Suppose they meet after T hrs time.So,20T+100/3 T=100.We ger T=15/8 .
So,Train X would travel 20*15/8=37.5 km before meeting Train Y. I don't understand is how it came out to be 15/8 . I understand that we take out speed . After that I am confused
Thanks for help
gmat-admin's picture

Let's take it from 20T + (100/3)(T) = 100 (where T = the time each train travels until they meet)

Eliminate the fraction by multiplying both sides by 3.
We get: 60T + 100T = 300
Combine: 160T = 300
Solve: T = 300/160 = 30/16 = 15/8

So, each train travels for 15/8 hours

Since train X travels at 20 km per hours, its travel distance = (speed)(time) = (20)(15/8) = 300/8 = 150/4 = 37.5 km

Jerry and Jim run a race of 2000 m. First, Jerry gives Jim a start of 200m and beats him by 30 seconds. Next, Jerry gives Jim a start of 3mins and is beaten by 1000m. Find the time in minutes in which Jerry and Jim can run the race seperately?

A. 8,10
B. 4,5
C. 5,9
D. 6,9
E. 7,10

1st off, the Jerry and Jim question still gives me nightmares at night. I straight up hate that question now.

This question however was much more to my liking.
Furthermore, out of a silly mistake I ended up finding a much easier solution.

Upon reading the question I assumed, wrongly, that the 2k distance meant 2000km. Then I assumed a value for Bee's speed, 100kmph, then naturally Anne's speed was 400kmph.
This allowed some easy arithmetic which left me with 800km as an answer; Foolishly now I checked the answer choices and found that K was in fact a variable. So I just multiplied and divided 800 by 1000. (which is 2k without the 2) replaced the numerator 1000 with K, and got 4k/5 .
Though later I realised that a much easier option would've been to see which of the answers gave me an 800 if I replaced the answer K's with 1000.
gmat-admin's picture

The Jim & Jerry question (here https://gmatclub.com/forum/jerry-and-jim-run-a-race-of-2000-m-first-jerr...) is a killer. Hopefully, the nightmares will subside soon :-)

As for the Ann & Bea question (here https://gmatclub.com/forum/ann-and-bea-leave-townville-at-the-same-time-...), it never dawned on me (when I created the question) that 2K might be misinterpreted as 2000, but I can totally see it now. That said, the test-makers would never assume that test-takers are aware that we can use "2K" to represent 2000

Once you realized your error, I like how you were able to use your existing calculations to determine the correct answer. Good stuff!

My quick intuition-based response was that if Ata traveled at 100km/h and arrived 1hour ahead of Carl who did 75km/h, Ata must have gained 25km over Carl in each hour and at the end of the third hour when Ata must have traveled 300km, the cumulative distance gained over Carl should be 75km.
gmat-admin's picture

Great logic!

Hi Brent,

The current in a river is 4 mph. A boat can travel 20 mph in still water. How far up the river can the boat travel if the round trip is to take 10 hours?

A. 69 miles
B. 88 miles
C. 96 miles
D. 100 miles
E. 112 miles

My question concerns assigning the “time” variable: When I set up the equation this way,

24(T1) = 16(10−T1)

I am confused as to why (it seems like it should not matter) if you set it up this way

24(10-T) = 16(T1)

As the time is the same - 10 hours! But it does matter and I get a different answer for the Time.

Is there something I am missing? How do you know which time (10 – T or T) to assign to which rate?
gmat-admin's picture

To avoid confusion, it helps to formally assign your variables.

In the equation 24(T1) = 16(10−T1), T1 represents the time spent traveling DOWNSTREAM at 24 miles per hour.

In the equation 24(10-T) = 16(T1), T1 represents the time spent traveling UPSTREAM at 16 miles per hour.

Does that help?


Yes! I was under the misguided impression that as long as the hours added to the "desired time" the variable assignment did not matter. Ok, got it, Thanks Brent! I had seen it done the wrong way before, and the person demonstrating the problem did not seem to explain or make it seem like it mattered as long as the total time was correct.

Brent sir, i just had a question. After i have completed all your videos, should i go for the egmat verbal course? do u recommend that?
gmat-admin's picture

Sorry, but I've never reviewed that course. I can tell you that our videos lessons cover everything you need to know for all sections of the GMAT.

Hi Brent, for the question below I need your approach of this lesson to figure this question out.


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