Train A leaves the station traveling at 30 miles per hour. Two hours

When train B catches train A, their location will be the same, and since they left the same point, their distance traveled will be the same.

RT = RT

30mph(T+2) = 40mph(T)

Solve for T. They meet after 6 hours. Plug 6 into either equation and get 240 miles

Hi , Can I know what level of question is that. Is it 600? Thanks.

I would say a bit higher - 650-660

Hi saraafifiahmed,

This question is a rare version of a "combined rate" question that is sometimes called a "chase down" question (and combined rate questions themselves a rare concept on the GMAT - you'll probably see just one question on it on Test Day). This specific prompt is a relatively easy variation (the speeds, time and answer choices are all round numbers), but the overall concept tends to fall at the higher end of the difficulty spectrum (even though this one is about as easy as the concept gets). You shouldn't worry too much about the difficulty level though - it's not going to be a big point gainer or point loser for you on the Official GMAT (if it shows up at all).

GMAT assassins aren't born, they're made,
Rich

Using the RTD chart we get:

..........R........T.........D
A........30.......T............
B........40......T-2..........

So, since we want the distance to be the same, we equate the 2 and find time:

30T = 40 (T-2)
30T = 40T - 80
80 = 10T
T=8

Substituting 8 in the equation for disrance for A we get:
30T = 30*8 = 240.

So, ANS B.

Hi all,

Is the following solution/logic correct? Please comment.

Time for which A travels = T + 2
Time for which B travels = T
Relative speed = 10 mph
Distance A travels in 2 hrs = 60 m

Hence, the time in which the gap between A and B "shrinks":

60 = 10 (T+2)
i.e. T = 4 hrs = when A and B meet

In 4 hrs, A traveled 180 m + initial 60 m = 240 m = ANSWER

TO

Hi thorinoakenshield,

Yes, your logic is correct - it is a little 'thicker' than it needs to be, but that's okay as long as you're comfortable with the 'steps' involved.

In real basic terms, Train A has a 60 mile "head start" when Train B gets moving. Since the speeds of the two trains are 30mph and 40mph, Train B will "make up" 10 miles every hour.

60 miles = (10mph)(T)
6 hours = T

So, 6 hours after it starts, Train B will catch up to Train A.

(6 hours)(40mph) = 240 miles

Final Answer:

GMAT assassins aren't born, they're made,
Rich

The question: What is the distance from the station where 2 trains meet?

* The speed difference between train A and B is 40 - 30 = 10mph, meaning in every hour,train B covers 10 miles compared to train A.
* In 2 hours train A covers 30mph*2h = 60miles. This is also the distance between 2 trains. Therefore, train B needs to go 60miles/10mph = 6hours to catch up train A.
* In 6 hours, train B goes 40mph * 6hours = 240 miles = where 2 trains meet.

Question: What is the distance where B passes A?

A and B go same direction.
In 2 hours, A go 2h* 30mph = 60 miles.B starts after A goes 2 hours. So the gap between A and B is 60 miles. (1)
B goes faster than A 10mph, meaning in each hour the gap shrinks 10 mile. (2)
From (1) and (2), the total gap = 0 in 60miles/10 miles = 6 hours, meaning B catches A in 6 hours.
Therefore, the distance where A and B meet is 6 hours * 40 mph = 240 miles.

Relative Speed = 40 - 30 = 10 Miles per hour
Relative Distance to be overcome = Distance travelled by A in 2 hours before B started = 2*30 = 60 Miles

Time for B to overtake A = Relative Distance / Relative Speed = 60 / 10 = 6 hours

Distance Travelled by B in 6 hours = 40*6 = 240 Miles.

Answer: Option B

for me it is easier to do the straightforward math, since I have problems with the relative speed concept

in 2 hours train A travels 60 mi.
So train B must cover those 60 mi and the distance the train A covers while train B is busy with the first 60 mi

40t=60+30t, t=6. In 6 hours B will travel 40*6=240 miles.

Train A----->
Train B----->

Realtive speed same direction
Add distance/Subtract rates
Relative distance/Relative rate

Relative distance at start of Train B
30*2=60
Relative rate
40-30=10

60/10=6

6+2=8

PITA (Plugging In The Answers)

I like trying B and D. Let's start with B.
(B) A travelled a total of 240 miles. At 30 mph, that's 8 hours. B was travelling two hours less. So 6 hours. At 40 mph. So 240 miles. Is that the same distance? Yep.

Answer choice B.


ThatDudeKnowsPITA

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