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Paul walks from home to work at a rate of 5 mph and bikes home from work along the same route at 12 mph. What is his average speed for the round trip?
- a)7/2
- b)90/17
- c)120/17
- d)17/2
- e)9
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Paul walks from home to work at a rate of 5 mph and bikes home from wo...
Since we have an average rate question we can use the following formula:
average rate = total distance / total time
Since the distance is the same in both directions, we can use a smart number to represent the one-way distance. A good number to use would be one that is divisible by both 5 and 12, so we can let the distance each way = 60.
So, the time going to work is 60/5 = 12, and the time going home from work is 60/12 = 5.
Finally we can determine the average rate:
average rate = total distance / total time
average rate = (60 + 60)/(12 + 5)
average rate = 120/17
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Community Answer
Paul walks from home to work at a rate of 5 mph and bikes home from wo...
Understanding Average Speed
To find the average speed for the entire round trip, we need to consider both the distance and the time taken for each leg of the journey.
Distance Calculation
- Let the one-way distance from home to work be "d" miles.
- Therefore, the total round trip distance is:
Total Distance = d (to work) + d (back home) = 2d miles
Time Calculation
- Time taken to walk to work:
Time (walk) = Distance / Speed = d / 5 hours
- Time taken to bike home:
Time (bike) = Distance / Speed = d / 12 hours
- Total Time for the round trip:
Total Time = Time (walk) + Time (bike) = d/5 + d/12
Finding a Common Denominator
- The least common multiple of 5 and 12 is 60.
- To combine the times:
d/5 = 12d/60
d/12 = 5d/60
- Therefore, Total Time = (12d/60) + (5d/60) = (17d/60) hours
Average Speed Formula
- The average speed (S) is given by the formula:
Average Speed = Total Distance / Total Time
- Substituting the values:
Average Speed = 2d / (17d/60)
Simplifying the Average Speed
- The "d" cancels out:
Average Speed = 2 / (17/60) = 2 * (60/17) = 120/17 mph
Conclusion
Thus, the average speed for Paul’s round trip is 120/17 mph, which corresponds to option 'C'.
To find the average speed for the entire round trip, we need to consider both the distance and the time taken for each leg of the journey.
Distance Calculation
- Let the one-way distance from home to work be "d" miles.
- Therefore, the total round trip distance is:
Total Distance = d (to work) + d (back home) = 2d miles
Time Calculation
- Time taken to walk to work:
Time (walk) = Distance / Speed = d / 5 hours
- Time taken to bike home:
Time (bike) = Distance / Speed = d / 12 hours
- Total Time for the round trip:
Total Time = Time (walk) + Time (bike) = d/5 + d/12
Finding a Common Denominator
- The least common multiple of 5 and 12 is 60.
- To combine the times:
d/5 = 12d/60
d/12 = 5d/60
- Therefore, Total Time = (12d/60) + (5d/60) = (17d/60) hours
Average Speed Formula
- The average speed (S) is given by the formula:
Average Speed = Total Distance / Total Time
- Substituting the values:
Average Speed = 2d / (17d/60)
Simplifying the Average Speed
- The "d" cancels out:
Average Speed = 2 / (17/60) = 2 * (60/17) = 120/17 mph
Conclusion
Thus, the average speed for Paul’s round trip is 120/17 mph, which corresponds to option 'C'.
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Paul walks from home to work at a rate of 5 mph and bikes home from work along the same route at 12 mph. What is his average speed for the round trip?a)7/2b)90/17c)120/17d)17/2e)9Correct answer is option 'C'. Can you explain this answer?
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