Train A left Centerville Station, heading toward Dale City Station, at

Question

Train A left Centerville Station, heading toward Dale City Station, at 3: 00 p.m. Train B left Dale City Station, heading toward Centerville Station, at 3: 20 p.m. on the same day. The trains rode on straight tracks that were parallel to each other. If Train A traveled at a constant speed of 30 miles per hour and Train B traveled at a constant speed of 10 miles per hour, and the distance between the Centerville Station and Dale City Station is 90 miles, when did the trains pass each other?

A. 4: 45 p.m.
B. 5: 00 p.m.
C. 5: 20 p.m.
D. 5: 35 p.m.
E. 6: 00 p.m.

A. 4: 45 p.m.
B. 5: 00 p.m.
C. 5: 20 p.m.
D. 5: 35 p.m.
E. 6: 00 p.m.

BrentGMATPrepNow · Accepted Answer

3:00pm  - Train A (traveling 30 miles per hour) left Centerville Station, heading toward Dale City Station 
If the train travels 30 miles EVERY HOUR, then it travels 10 miles every 20 minutes (since 20 minutes = 1/3 hours) 
In other words, at 3:20pm, Train A has already traveled 10 miles. 
So,  at 3:20, the trains are now 80 miles apart .

3:20pm  - Train B (traveling 10 miles per hour) left Dale City Station heading toward Centerville Station 
At this point (at 3:20pm), the trains are 80 miles apart.
Also,  every hour , Train A moves 30 miles toward train B, and Train B moves 10 miles towards train A. This means the gap between them is decreasing at a rate of 40 miles per hour.

At this rate, the 80-mile gap will be reduced to zero miles (i.e., the trains meet) in 2 hours.

So, the trains will meet at  3:20pm  + 2 hours = 5:20pm

Answer: C

kplusprinja1988 · Answer

the distance travelled by the train A in first 20 minutes will be 10.
The distance which will be remaining is 80.
Now both trains are running in opposite direction.Their speed will be added so 40.
Time at which they will meet =80/40=2
time of train B will be 3:20 +2=5:20

Hence answer is C.Hope i am correct

CounterSniper · Answer

as per the question
train A left Centerville Station, heading toward Dale City Station, at 3: 00 p.m
and
Train B left Dale City Station, heading toward Centerville Station, at 3: 20 p.m
Distance between the two stations = 90 miles
speed of train A =30 mile per hour
speed of train B =10 mile per hour
Relative speed = 40 mile per hour(since they are travelling in opposite direction)
relative distance = 90 -(distance travelled by train A in 20 minutes)
 = 90 -10 = 80 miles
thus time taken = 80/40=2 hours from 3:20 pm =5:20 pm

Nunuboy1994 · Answer

Bunuel  okay one thing I don't like about this question that I was hoping you could clear up- I came up with the original formula at first

Distance traveled by A + Distance traveled by B = Length between Centerville and Dale

A =30 (x +20)
B= 10(x)

30x +600 + 10x = 90 - this obviously didn't seem right but in another similar problem they expressed the equation this way? Like instead of below where I write 30(x +1/3) they put the actual amount of minutes? How do we distinguish? Do we just intuitively pick smart numbers?

A= 30(x + 1/3)
B = 10(x)

30x + 10 + 10x =90
40x= 80
x= 2 hours

2 hours + 20 minutes=

C

Bunuel · Answer

30 and 10 are rates in miles per  hour , so in (rate)(time) = (distance), the (time) must also be in in hours, the same way x above is the number of hours, not minutes.

JeffTargetTestPrep · Answer

Since 20 minutes = 1/3 hour, we can let the time of Train B = t hours, and thus Train A = t + 1/3 hours.

The distance for Train A is 30(t + 1/3) = 30t + 10, and the distance for train B is 10t; thus:

30t + 10 + 10t = 90

40t = 80

t = 2 hours

So, the trains passed each other at 3:20 + 2 hours = 5:20 p.m.

Answer: C

Blackbox · Answer

Jeff - Thanks for answering. May I question as to why you added 2 hours to 3:20 instead of 3:00?

Zillur raihan · Answer

i have a different suggestion 
after 2 hours at 5
train A will be crossing 60 miles and B will be 17.** miles
than after 20 min A will cross 70 mile and B will 20 mile 
which is the total length 90 mile
so the ans will be 5.20

zoechrys · Answer

Hi,

I used the same technique but somehow got a difference solution. Adding the 20min in the the time of Train A or subtracting the 20 min from the time of Train B should result in the same solution no? 
It obviously doesn't here but I was wondering why as I have done it this way several times and got the right answer for other exercises.

90 = 30(t) 90 = 10 (t-1/3)

30(t) + 10(t) - 10/3 = 90

40t = 90 + 10/3

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 left Centerville Station, heading toward Dale City Station, at

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 left Centerville Station, heading toward Dale City Station, at

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