M07-11

Question

A train traveling at a consistent speed takes 30 seconds more to cover 2 kilometers than what it would take to cover 4 kilometers at a speed of 120 kilometers per hour. What is the speed of the train in kilometers per hour?

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

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

Bunuel · Accepted Answer

Official Solution:

A train traveling at a consistent speed takes 30 seconds more to cover 2 kilometers than what it would take to cover 4 kilometers at a speed of 120 kilometers per hour. What is the speed of the train in kilometers per hour?

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

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

The time required to travel 4 kilometers at 120 kilometers per hour is given by  	ext{time} = \frac{	ext{distance}}{	ext{rate}} = \frac{4}{120}  hours or   \frac{4}{120}*3,600 = 120  seconds.
 
The time required to travel 2 kilometers at the train's consistent speed is  120 + 30 = 150  seconds, or  \frac{150}{3,600} = \frac{1}{24}  hours.
 
Thus, the speed of the train is  	ext{rate} = \frac{	ext{distance}}{	ext{time}} = \frac{2}{(1/24)} = 48  kilometers per hour.

Answer: C

gracie · Answer

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

cyb · Answer

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

VAKRATUNDA · Answer

The question is absolutely 700 level. Great Language trap.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

MBAToronto2024 · Answer

KarishmaB  
Hmmmm....I got into a trap. 
30/3600 = 1/120 h

so we have: 
1/30h 4km 120 km/h -> 1/60h 2km 120km/h

1/120 + 1/30 h -> 1/40h. It's the time with 30 additional seconds.

Then 1/40 * x = 2 -> x - 80 km/h

Where did I make a mistake?

KarishmaB · Answer

I am not sure what and how you did there. Note that the two instances are separate and we might as well have had different trains. The two speeds, time taken and distances are different. Case 1: It covers 4 kilometers at a speed of 120 kilometers per hour. Time taken = 4/120 = 1/30 hrs = 2 mins Case 2: It takes 30 secs extra to cover 2 kms at another speed. 30 seconds extra means the time taken = 2 mins 30 secs = 2.5 mins Distance covered = 2 kms Speed = \frac{2}{2.5/60} = 48 kmph Answer (C) Discussion on TSD: https://youtu.be/7ASEIvxYPCM

phmahi1997 · Answer

I like the solution - it’s helpful.

phmahi1997 · Answer

I like the solution - it’s helpful.

phmahi1997 · Answer

I like the solution - it’s helpful.

Aboyhasnoname · Answer

Hi  Bunuel  Please can you help where I am going wrong....

If a train takes 30 seconds more for 2 kms ..then it means ...it takes 1 min more for 4 kms...means 30 mins more for 120 kms....
So ..travelling at 120km/hr.......time is 1 hour for 120 ...and the slower speed...takes 30 mins more ...means 1.5 hours for 120...so the ratio of time is 2:3....Now the ratio of speed of Faster to slower should be 3:2 ...Faster is 120..Slower should be 80.......
Can you please help where is it it that I am going wrong in his approach?

Bunuel · Answer

Your method is wrong because you’re applying the scaling incorrectly.

At 120 km/h, the train takes 60 minutes to cover 120 km. The scaling factor from 4 km to 120 km is 30, so both the distance and the time difference scale by 30.

That means the slower train will take 30 * 30 = 900 seconds (15 minutes) more to cover 2 * 30 = 60 km than the faster train does for 120 km. This gives 75 minutes for 60 km, and doubling the distance gives 150 minutes for 120 km.

The ratio of times is 150 to 60, or 5 to 2. Hence, the speed ratio is also 5 to 2, giving the slower train’s speed as 48 km/h.

M07-11

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