Questuin: A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round trip?
- 32.0
- 33.0
- 34.3
- 35.5
- 36.5
“A car travels from Mayville to Rome at an average speed of 30 miles per hour”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide Quantitative Review". To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. GMAT Quant section consists of 31 questions in total. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.
Solution and Explanation
Approach Solution 1:
It is asked, A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round trip?
Probability is calculated as the sum of all probable outcomes.
Calculating the total distance and the total time, then dividing the total distance by the total time, is the proper approach to determine the average speed.
In this scenario, let D be the one-way distance. Thus, the overall distance is 2D. (travelled over the same route twice)
Total Time = Travel Time for Distance D at 30 mph + Travel Time for Distance D at 40 mph
\((D/30) + (D/40)\)
7D / 120
This means, avg speed = Total distance/total time
= (2D) / (7D / 120)
= 34.285
= 34.3
Correct Answer: C
Approach Solution 2:
There is another approach to answering this question
It is asked, A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round trip?
For the distance between Mayville and Rome, pick a logical number: 120 miles should be the distance considering that this distance is suitable for both 30 and 40 mph.
Since we know
Time = distance/speed
So, time from Mayville and Rome (at 30 mph) = 120/30 = 4 hours
Time from Rome to Mayville (at 40 mph) = 120/40 = 3 hours
This means
Average speed = (total distance traveled)/(total time)
= (120 + 120)/(4 + 3)
= 240/7
≈ 34.3
Correct Answer: C
Approach Solution 3:
It is asked, A car drives at an average speed of 30 miles per hour from Mayville to Rome and then promptly makes its way back at an average speed of 40 miles per hour. Which of the following comes closest to the average speed for the round journey, measured in miles per hour?
The total of all likely outcomes is how probability is computed.
The correct method to get the average speed is to calculate the entire distance and the total time, then divide the total distance by the total time.
Let D represent the one-way distance in this case. The whole distance is therefore 2D. (took the exact same way twice)
Total time is the sum of the travel times for the distance D at 30 mph and 40 mph.
7D / 120
Accordingly, average speed is calculated as follows:
Total distance/total time = (2D) / (7D / 120) = 34.285 = 34.3
Correct Answer: C
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