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16 Sep 2014, 00:39
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In the morning, John drove to his mother's house in the village at an average speed of 60 kilometers per hour. When he was going back to town in the evening, he drove more cautiously and his speed was lower. If John went the same distance in the evening as in the morning, what was John's average speed for the entire trip?
(1) In the evening, John drove at a constant speed of 40 kilometers per hour.
(2) John's morning drive lasted 2 hours.
(1) In the evening, John drove at a constant speed of 40 kilometers per hour.
(2) John's morning drive lasted 2 hours.
16 Sep 2014, 00:39
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Official Solution:
In the morning, John drove to his mother's house in the village at an average speed of 60 kilometers per hour. When he was going back to town in the evening, he drove more cautiously and his speed was lower. If John went the same distance in the evening as in the morning, what was John's average speed for the entire trip?
The average speed is equal to \(\frac{\text{total distance} }{\text{total time} }\).
Say the distance between the town and the village is \(d\) kilometers, and the speed from the village to town is \(x\) kilometers per hour, then \(\frac{\text{total distance} }{\text{total time} }=\frac{d+d}{\frac{d}{60}+\frac{d}{x} }\). \(d\) can be reduced, and we get \(\text{speed}=\frac{2}{\frac{1}{60}+\frac{1}{x} }\). So, as you can see we only need to find the average speed from the village to town.
(1) In the evening, John drove at a constant speed of 40 kilometers per hour. Sufficient.
(2) John's morning drive lasted 2 hours. We know nothing about his evening drive. Not sufficient.
Answer: A
In the morning, John drove to his mother's house in the village at an average speed of 60 kilometers per hour. When he was going back to town in the evening, he drove more cautiously and his speed was lower. If John went the same distance in the evening as in the morning, what was John's average speed for the entire trip?
The average speed is equal to \(\frac{\text{total distance} }{\text{total time} }\).
Say the distance between the town and the village is \(d\) kilometers, and the speed from the village to town is \(x\) kilometers per hour, then \(\frac{\text{total distance} }{\text{total time} }=\frac{d+d}{\frac{d}{60}+\frac{d}{x} }\). \(d\) can be reduced, and we get \(\text{speed}=\frac{2}{\frac{1}{60}+\frac{1}{x} }\). So, as you can see we only need to find the average speed from the village to town.
(1) In the evening, John drove at a constant speed of 40 kilometers per hour. Sufficient.
(2) John's morning drive lasted 2 hours. We know nothing about his evening drive. Not sufficient.
Answer: A
