A tale of two trains

[Stormgal]

An express train traveled at an average speed of 100 kilometers per hour, stopping for 3 minutes after every 75 kilometers. A local train traveled at an average speed of 50 kilometers, stopping for 1 minute after every 25 kilometers. If the trains began traveling at the same time, how many kilometers did the local train travel in the time it took the express train to travel 600 kilometers?

a. 300
b. 305
c. 307.5
d. 1200
e. 1236

Does anyone know of a shortcut to this? This problem seems to be very tedious!


Also, does anyone know if the GMAT makes one go thru this type of tedious calculation?

[Mercedes2004]

Hi Stormgal:

the answer is C: 307,5 km
I don't think is so tedius (not easy anyway)
Here is my solution

Express Train:
600 km --> 6 hours (since 100 km/h) + stops * 3 min.
stops = 600 / 75 = 8, but as it is an integer number, the last stop in km 600 is not a real stop, so it would be 7 stops
so, time= 6 hours + 7 * 3 min. = 6 hours 21 min

Local Train:
in 6 hours, it will make 300 km (since its speed is 50 km/hour)
in 300 km it will have 300 / 25 stops = 12, 12 stops 1 min each = 12 min
we have 6 hours 12 min, but we need to calculate how many km can it make in 6 hours 21 min, so 21-12 = 9 min
if 60 min it can make 50 km, 9 min it can make 7,5 km
so, the distance is 300 + 7,5 = 307,5 km

It took me more to write it here than actually solving it

[inatrance]

this is a good question. Not impossble, but I agree that it took me a bit longer than 2 minutes. This is the kind of question that could waste a lot of my time as I macho-ly insist of powering my way through it. My personal pref would be to straight awau spot that the distance has to be 300 miles in the 6 hours, 21 mins (easy to figure out and already you are in the right ball park, narrowing it down to 2 possible answers: b & c), and then if I'm not confused at that point, spend some time deciding it if its an additonal 5 miles or 7,5 miles, just like Mercedes explained.

[Sargataur]

why in the case of the express train u discount the last stop (ie. stop. no 8) of 3 mins but u take that into consideration in the case of thel ocal train (25 stops) ...why not 24 for local as well...

im dense please exlpain

[n_adroja]

Hi Mercedes,

can u pls explain y you do not apply the same rule of calculating the stops in both Local train as well as express train?
thanks
adroja.

Originally Posted by Mercedes2004

Hi Stormgal:

the answer is C: 307,5 km
I don't think is so tedius (not easy anyway)
Here is my solution

Express Train:
600 km --> 6 hours (since 100 km/h) + stops * 3 min.
stops = 600 / 75 = 8, but as it is an integer number, the last stop in km 600 is not a real stop, so it would be 7 stops
so, time= 6 hours + 7 * 3 min. = 6 hours 21 min

Local Train:
in 6 hours, it will make 300 km (since its speed is 50 km/hour)
in 300 km it will have 300 / 25 stops = 12, 12 stops 1 min each = 12 min
we have 6 hours 12 min, but we need to calculate how many km can it make in 6 hours 21 min, so 21-12 = 9 min
if 60 min it can make 50 km, 9 min it can make 7,5 km
so, the distance is 300 + 7,5 = 307,5 km

It took me more to write it here than actually solving it

[kalipegasus]

becos Sargatur,
We are calculating the kms travelled by local train.. we are not calculating the time taken by him.. we have laready calculated the time .. which is 6 hrs 21 min.. this is constant..for both the trains now.. the variable is distance... and that is calculated by noting that every 50kms the local train takes 1 hr 2min..hence in 6 hrs 12 min it will move 300 kms and remaining 9 min it will move 7.5 kms

Answer is therefore : C

[Mercedes2004]

Another explanation could be that for the E. train, the last stop means the end of the journey (600 km), so it is not needed to include it, meanwhile, for the L. train the last stop ocurrs 9 min. before the E train arrives at the last stop. So the last stop of the L train ocurrs while the other train is still traveling, and the L train will travel for 9 min more.

[slkreddy]

600/75 = 8
7 stops
7*3 + 6= 6 hr 21 min
for 6 hrs ,it travels 300km and it stops for 12min
6hr12min ------------ 300km
9min------7.5km
total =307.5