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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.
m09 q15
(1) In the evening, John drove at a constant speed of 40 kilometers per hour.
(2) John's morning drive lasted 2 hours.
m09 q15
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22 Mar 2013, 13:17
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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
30 Jul 2013, 17:17
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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.
When getting the average speed of two or more speeds, the distance (think of it like a weighted average) comes into play. In this case, the distance is the same for both speeds as he is traveling a route then traveling in the opposite direction on said route.
SUFFICIENT
(2) John's morning drive lasted 2 hours.
This allows us to get the distance of the route but we don't know how fast he drove on the return home.
INSUFFICIENT
(A)
(1) In the evening, John drove at a constant speed of 40 kilometers per hour.
When getting the average speed of two or more speeds, the distance (think of it like a weighted average) comes into play. In this case, the distance is the same for both speeds as he is traveling a route then traveling in the opposite direction on said route.
SUFFICIENT
(2) John's morning drive lasted 2 hours.
This allows us to get the distance of the route but we don't know how fast he drove on the return home.
INSUFFICIENT
(A)
