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?
- 300
- 305
- 307.5
- 1200
- 1236
“An express train traveled at an average speed of 100 kilometers per hour”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “Master the GMAT CAT”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.
Solution and Explanation:
Approach Solution 1:
It is asked 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?
Evaluating further –
The Time taken by the express train to cover is 600 km :
=(\(\frac{600}{100}\)) hrs = 6 hrs
Total stoppages = (600 75) - 1 = 7
Stoppage time: (3 x 7 min) = 21 min
Time spent: 6 hours and 21 minutes.
50 km of local train travel (with stops) took 1 hour and 2 minutes in total.
Thus, the local train travels (50 × 6) = 300 km in 6 hr 12 min
In the remaining 9 min, train covers =(5060×9) km=7.5 km
Therefore Required distance = (300 + 7.5) km = 307.5 km
Correct Answer: C
Approach Solution 2:
There is another approach to answering this question
Effective travel time by express train for 75 kilometres = [\(\frac{60}{100}\)*75+3] mins
= 48 min
Time takes to travel 600 km = [48 * 7 + 45] min
=336 +45 min
381 min
Effective travel time by local rail for 25 kilometres is 31 minutes.
Therefore
Travel distance in 9 minutes is \(\frac{50}{60}\)*9
=75 km
Covered distance in (31 * 12) minutes
= 12 × 25 = 300 kilometres
Total mileage equals 307.5 km (300 + 7.5 km).
Correct Answer: C
Approach Solution 3:
Express Train:
600/100= 6 hours without stop
600/75= 8, so it must have had 7 stops
So the total time= 6 x 60 + 3 x 7 = 381 minutes.
Locak train travels at 50 km/h = (5/6) km/minute.
In 360 minutes, it will travel 300 km.
At every 25 km, there will bw a stop. So, while travelling 300 km, it will stop 300/25 = 12 stops.
Now, we have (360 + 12) minutes to travel 300 kms and we need to know what distance the train will travel in the remaining 9 minutes.
Distance = (5 x 6) x 9 = 15/2 = 7.5 km.
Therefore, local train teavelled 300 + 7.5 = 307.5 km.
Correct Answer: C
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