An express train traveled at an average speed of 100 kilometers per ho

Question

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

A. 300
B. 305
C. 307.5
D. 1200
E. 1236

Maria240895chile · Answer

Express train
R*T=D
100*x=600
x=6

but we need to add the time that the train stop every 75 km which is 3 min. 
600 km divided by 75km = 8 which means that the train made 7 stops.

7*3min=21 min
 \frac{21}{60}=\frac{7}{20}=\frac{3,5}{10}=0,35hr

so the time that takes the express train to travel 600km is the time traveled+the time stoped. 6+0,35=6,35hr

now for the local train
R*T=D
50*6,35=317,5

in this case, opposite to the first case, we have to subtract the stops of the local train. We know that every 25km the train made a stop of 1 min. 317,5 is aprox 318 so  \frac{318}{25}=\frac{63}{5}=13 min.aprox

Now from total time take out the  13 min=\frac{13}{60}hr . 
 6,35hr-\frac{13}{60}hr=6,14 hr . This is the time were the local train was in movement.

so again R*T=d
50*6,14=307 aprox

IMO C

A_Nishith · Answer

Express Train  100  km/hr : 
600km / 75 km = 8 Runs of 75km each
Time taken = 8*(75/100) + 7 halts of 3 min each in between
 = 6 hrs + 21 mins

Passenger Train @ 50km/hr :
Distance covered in 6 hr 21 min = ?
Each stretch of 25 km (given) => 25/50 hr = 30 hr run each time

When broken 6 hr 21 min = { 30+1+ 30+1+ 30+1+ 30+1+ 30+1+ 30+1+ 30+1+ 30+1+ 30+1+ 30+1+ 30+1+ 30+1+ 9 } min = (12*30) + 12* (1 min halt) + (21-12 = 9) min

Therefore, Distance covered = 12* (0.5*50) + (9/60)*50 = 300 + 7.5 
 = 307.5 kms
Ans: C

mattisweb · Answer

How we can assume that the average speed of the trains is not calculated accounting for the stoppages (as in, a trick question with answer A). After all, definition of average speed would account for stoppages as well. I would agree with the solution if it said "speed of train when moving".

nectar12 · Answer

Marrisweb I was thinking same

PSKhore · Answer

We first need to calculate the total time the first train takes to travel 600 km + resting time.
Travelling at 100 kmph, it should take 6 hours to travel 600 km, the resting time would be 600/75 = 8 resting points, but the last 3 min should not be considered since it has reached 600 km, so 7*3 = 21 min

Total time = 6 hours + 21 minutes

For the second train, it travels 50 kmph, so in 6 hours it travels 300 km.
To calculate the resting points = 300/25 = 12, each of 1 min, so 12 minutes
Leftover time = 21 - 12 = 9 min
If it travels 50 km in 1 hour, in 9 min it travles 7.5 km

So, total distance is  307.5 km

Adit_ · Answer

How are we considering the fact that avg speed is excluding the stoppages? Definition of avg speed is Total Distance upon Total Time and nowhere is it mentioned that the avg speed is devoid of the stoppages mentioned. Kindly help me out.

An express train traveled at an average speed of 100 kilometers per ho

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An express train traveled at an average speed of 100 kilometers per ho

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