Question: A train travels from Albany to Syracuse, a distance of 120 miles, at an average rate of 50 miles per hour. The train then travels back to Albany from Syracuse. The total traveling time of the train is 5 hours and 24 minutes. What was the average rate of speed of the train on the return trip to Albany?
- 60 mph
- 50 mph
- 48 mph
- 40 mph
- 35 mph
Correct Answer: D
Solution and Explanation
Approach Solution 1:
This question has only one approach
Given that a train travels from Albany to Syracuse, a distance of 120 miles, at an average rate of 50 miles per hour. The train then travels back to Albany from Syracuse. The total traveling time of the train is 5 hours and 24 minutes.
Now it is asked what will be its average rate of speed on the return trip to Albany.
First, we have to consider the units of measurement.
The distance is given in miles.
The speed is given in miles per hour.
Time is given in hours and minutes.
It should be noted that the options are given in miles per hour, so we should solve the problem in the same units.
Every data is in its correct unit except the time. It has to be converted into hours.
Given total time = 5 hours and 24 minutes.
It is important to convert 5 hours 24 minutes to only hours as the answers are not given in minutes.
We know that 60 minutes is 1 hour
=> 60 min = 1 hour
For 24 minutes,
24 minutes = 24 mins * 1 hour/60 mins = 4/10 hour = 0.4 hour
Total time (whole journey) in hours = 5 hours + 0.4 hours = 5.4 hours
Now total time of journey = 5.4 hours
Note that this time is the total of both - the forward journey and the return journey.
We have to calculate the total time taken for the return journey.
Let the time taken for forward journey (Albany to Syracuse) be T1 and the return journey be T2.
Time taken to go from Albany to Syracuse = distance / speed during journey
T1 = 120 miles/ 50 miles per hour = 2.4 hour
We know that T1 + T2 = 5.4 hour
T2 = 5.4 - T1
Putting the value of T1 we get
T2 = 5.4 - 2.4 = 3 hours
So the time taken for the return journey is 3 hours.
It is asked to calculate the average rate of speed during the return journey.
The average rate of speed is related to distance and time as
Average speed = total distance traveled/ total time taken
In the return case, the total time taken is 3 hours.
Average speed during return journey = 120 miles/ 3hours = 40 miles per hour.
Therefore the average rate of speed of the train during the journey of the return trip to Albany is 40mph. The correct answer is D
“A train travels from Albany to Syracuse, a distance of 120 miles”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.
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