Official Solution:

A train traveling at a certain constant speed takes 30 seconds longer to travel 2 kilometers than it would take to travel 4 kilometers at 120 kilometers per hour. At what speed, in kilometers per hour, is the train traveling?

A. 24
B. 40
C. 48
D. 96
E. 120


Time to travel 4 kilometers at 120 kilometers per hour is \(\text{time}=\frac{\text{distance}}{\text{rate}}=\frac{4}{120} \text{hours} = \frac{4*3,600}{120} \text{seconds} = 120 \text{seconds}\);

Time to travel 2 kilometers at a regular speed is \(120+30 = 150 \text{seconds} = \frac{150}{3,600} = \frac{1}{24} \text{hours}\);

So, the speed of a train is \(\text{rate}=\frac{\text{distance}}{\text{time}}=\frac{2}{(1/24)}=48\) kilometers per hour.


Answer: C
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seems like a 700 level problem, not sub-600.

let s=speed
2/s-4/120=1/120
s=48 kph

time taken for second train travelling at 120Kmph= 4/120 = 1/30 hr

Total time for the first train travelling at x speed = 30/3600 + 1/30 = 1/24 hr

speed = distance /time= 2km/(1/24) hr = 48 kmph

The question is absolutely 700 level. Great Language trap.

Bunuel don't you think the language of the question can also lead to such an approach below -

Train with 120kmph takes 120 sec to cover 4 km
i.e. 30 sec per km. hence, 60 sec for 2 km

Now the other case -
as stated in question it takes 30 sec more to travel 2km, than the previous train.
mean this time it takes 60 + 30 = 90 sec for 2km.
so now speed is (2*60*60\90) = 80 kmph

Bunuel, can you please help answer this question? I have the exact same question - why can it not be 80km/hr?

the language is a bit mis-leading..
read twice if u dont get. no problem.

there are two trains.
train 1- at certain speed (which we need to find)
train 2- at 120km/hr.

train 1 takes more time than train 2 (linking point)
how they are linking?
train 1 takes more time to travel 2kms than train 2 to travel 4 kms..

bingo...
train 2 takes 120 sec to travel 4kms. (120kmph- 1hr is equal to 3600 sec)
train 1 takes 150 sec to travel 2kms.
by converting we get 48kmph

The language of the question is misleading!!

"Regular Speed" Poor wording on the explanation. Otherwise great question