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

Question

Train A leaves the station traveling at 30 miles per hour. Two hours later train В leaves the same station traveling in the same direction at 40 miles per hour. How far from the station was train A overtaken by train B?

(A) 180
(B) 240
(C) 270
(D) 300
(E) 320

(A) 180
(B) 240
(C) 270
(D) 300
(E) 320

KarishmaB · Accepted Answer

This question tests you on relative speed. 
Train A leaves the station traveling at 30 miles/hr. So it covers 30*2 = 60 miles in 2 hrs. After 2 hrs, train B leaves the station. When train B leaves the station, distance between train A and train B is 60 miles since train A has already traveled 60 miles.
Now train B needs to cover up this distance between them by traveling faster than train A. In one hour, train B covers 10 miles more than train A (because train B's speed is 10 miles/hr more than train A's speed). So train B will cover the extra 60 miles in 6 hours. 
Train A had traveled for 2 + 6 = 8 hrs before it was overtaken by train B. Hence, it had covered a distance of 8*30 = 240 miles.

PareshGmat · Answer

Answer = B = 240 Refer diagram below: train.png Train A has already travelled 60 miles when Train B starts Say total distance = x from originating point where both trains meet Time equation would be as follows: \frac{x-60}{30} = \frac{x}{40} x = 240

abmyers · Answer

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

saraafifiahmed · Answer

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

KarishmaB · Answer

I would say a bit higher - 650-660

EMPOWERgmatRichC · Answer

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

pacifist85 · Answer

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 .

thorinoakenshield · Answer

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

EMPOWERgmatRichC · Answer

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:  B

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

misanguyen2010 · Answer

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.

misanguyen2010 · Answer

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 t he 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.

GMATinsight · Answer

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

galiya · Answer

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.

fireagablast · Answer

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

ThatDudeKnows · Answer

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

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