A bullet train leaves Kyoto for Tokyo traveling 240 miles per hour at

B -

The bullet train will have travelled 240 x (10/60) miles after the first 10 minutes = 40 miles.

At 12:10 , the bullet train and the train are 260 miles apart (=300-40). To calculate when they will pass:

260 = 240*(60)*x + 160*(60)*x where x = the time it takes for them to reach one another in minutes

x = 39 minutes for the trains to pass each other AFTER 12:10.

Therefore the trains must have passed each other at 12:49

Let distance travelled by A be x miles
Speed A = 240/60 = 4 miles per minue
Speed B = 160/60 = 8/3 miles/min
time = distance/speed
Distance travelled by A in 10 minutes = 40 miles.

Distance remaining = 260 miles.

3x/8 = (260-x)/4
12x = 260.8 - 8x
x = 26.4 = 104

time = 39mins

Hence B

A bullet train leaves Kyoto for Tokyo traveling 240 miles per hour at 12 noon. Ten minutes later, a train leaves Tokyo for Kyoto traveling 160 miles per hour. If Tokyo and Kyoto are 300 miles apart, at what time wil the trains pass each other?

A. 12:40pm
B. 12:49pm
C. 12:55pm
D. 1:00pm
E. 1:05pm

thats an interesting , shorter approach, I got the same answer but im sure it took me longer

R=T*D

240t=d
160(t-1/6)=300-d

160t-160=300-240t

t=49/60

!)Train K starts from Kyoto at 12:00 noon. It moves at the speed of 240 mph. Say it covers 300-x miles

2)Train T starts from Tokyo at 12:10 PM at a speed of 160 mph. Say it covers the rest of x miles

From (1) we have 300-x = 240(t+1/6) [ we have "+1/6" here since Train K travels 10 minutes or 1/6 hours longer than train T]

and From (2) we have x=160t

combining above two equations:
300-160t=240t + 40
260 = 400t

t= 26/40 = 13/20 hours = (13/20)*60 = 39 mins.

12:10 + :39 = 12:49

Good method.

I did the long method too

(t+1/6) 240 + 160 t = 300

14) A bullet train leaves kyoto for Tokyo traveling 240 miles per hour at 12 noon. Ten minutes later, a train leaves Tokyo for Kyoto traveling 160 miles per hour.If Tokyo and Kyoto are 300 miles apart, at what time ill the trains pass each other?

a) 12.40 pm
b) 12.49 pm
c) 12.55 pm
d) 1.00 pm
e) 1.05 pm

Catch up time= Distance between the 2/Speed of Train from K->T + Speed of Train from T->K

300/240+160 = 45 mins
as Train from T->k started 10 mins late catch up time will be 12.55
If i calculate with other method

240(t+1/6)+ 160t = 300

i got t as 39 mins

as Train from T->k started 10 mins late catch up time will be 12.49

WHEN CAN WE APPLY THE FORMULA TO CALCULATE Catch up time because in this case its not giving correct answer.

300/240+160 = 45 mins ---> This is wrong
You are assuming that train K->T started the same instant that the train T->K started. So train T->K traveled 1/6 * 160 miles more and hence the "kiss" time went down by 4 mins. i.e. 45 mins. However the actual time to intersect is 49 mins.

as Train from T->k started 10 mins late catch up time will be 12.55 --->

When using the relative speed you assumed if one train were still, the other train will catch up at effectively 400 mph. So 400/6 miles is covered in 1/6 hr. This cannot be undone by simple arithmetic as adding 10 mins to the time of intersect. This doesn't work.

In fact the correct assumption is that for the first 1/6 hr (10 mins), the slower train was still and only the faster train was moving.

Let the trains meet after x hours.

240x + (x - 1/6)160 = 300

24x + 16x - 16/6 = 30

40x = 16/6 + 30

=> 40x = 196/6

=> 10x = 49/6

So it wil be after 49/60 hr or 49 min, so 12:49, hence the answer is 12:49 PM

train A-------------------B
r: 240 ------------------160
t: t+10/60=t+1/6 --------t (cause A moved 10 mins ealier)
S: 300-[240*(t+1/6)-----160 t
300-240t-40=160t so t=1 hour and 5 mins

from what i learned from MGMAT this is " the kiss/ crash"

train ----rate-----time-----distance
A---------a--------t--------at= A's distance
B---------b---------t-------bt=B's distance
total-----(a+b)-----t-------total distance covered
(add) ----the same----add

Time taken to meet = Distance/relative speed
Second train started 10 minutes later, the first train travels in 10 minutes = 240/60*10=40 miles
so they have to travel 300-40=260 miles
now, time= [260/(240+160)]*60= 39 minutes
as 10 minutes later 39+10=49 minutes

Ans. B

240(t +1/6) +160t = 300
t = 39 mins
t+10 = 49 mins
Answer is B.

Posted from my mobile device

This is a very beautiful question for any student of clear thinking. You could apply the right strategy/formular and blow the solution by an error in the not very short solution process.
Rate x Time = Distance
Either \(240t + 160(t - 1/6) = 300\)

OR \(240(t + 1/6) + 160t = 300\)

will give you the solution; the first gives you t = 49 and the second gives you t = 39.
The first is straight forward without a trap cos it came straight out from the wording of the question without manipulation.
You might say the second is great since you were aware that you must add \(\frac{(1}{6)}\)hours to it. Well,in a CAT, if you had got an answer choice that says 12:39pm then you might have fallen into the trap and FAILED THE QUESTION pitifully with your head held high.
I would always want to follow the question prompt like I'm not too smart.

Hi Nez,
You are absolutely correct that a Q like this can be blown to pieces if you take one wrong step..
If I were to do this, I will not get into making equation...
i will see how much distance is left between two when both are in motion..
1) in 10 min, train from K to T would have travelled= 240*10/60=40..
2) so distance between the two when Train starts from T to K= 300-40=260..
3) combined speed as both travelling towards each other= 240+160=400.
4) they will meet after= 260/400 * 60=39 minutes..
time after 39 minutes= 12:10+39 min=12:49..
This method too finally does what the equation does but slightly less error prone

[b]AS, later train start ten minutes later , so the first train(from Kyoto to Tokyo) cover distance in ten minutes equals

(240/60*10 ) 40 miles. Rest of the distance 300-40 = 260.therefore, two train together will cover up this distance

Relative speed will be (240 + 160) 400 Miles per hour. required time = (260/400*60) 39 minutes.

Total time would be 39+10 = 49 minutes . they will pass each other at 12: 49 pm.

Kudos if it helps.Thanks

Train 1 travels in 10 min = 40 Km
Total distance to travel when train 2 starts is = 300 - 40 = 260
Relative speed = S1 + S2 (travelling towards each other) = 240 + 160 = 400

Total time taken = (260 * 60) / 400 = 39 mins + 10 mins = 49mins therefore 12:49 pm is the answer

Given: A bullet train leaves Kyoto for Tokyo traveling 240 miles per hour at 12 noon. Ten minutes later, a train leaves Tokyo for Kyoto traveling 160 miles per hour.

Asked: If Tokyo and Kyoto are 300 miles apart, at what time will the trains pass each other?

Distance travelled by first train in 10 minutes = 240 *10/60 = 40 miles
Distance to be travelled = 300 - 40 = 260 miles
Relative speed of trains = 240 + 160 = 400 mph
Time taken to pass each other = 260*60/400 = 39 minutes

Time when train will pass each other = 12:00 + 0:10 : 0:39 = 12:49 PM

IMO B