Bunuel wrote:
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
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 kmNow 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