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Cyclist Speed Varies, maximum distance travel in 7 hours?

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Intern
Joined: 09 May 2011
Posts: 15
Cyclist Speed Varies, maximum distance travel in 7 hours?  [#permalink]

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11 Mar 2012, 15:14
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Difficulty:

5% (low)

Question Stats:

89% (00:40) correct 11% (00:54) wrong based on 122 sessions

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Source: Knewton
A cyclist's speed varies, depending on the terrain, between 6.0 miles per hour and 14.0 miles per hour, inclusive. What is the maximum distance, in miles, that the cyclist could travel in 7 hours?

(A) 42
(B) 56
(C) 70
(D) 98
(E) 140

Here is my question, when a problem states that "speed varies," doesn't that mean that the biker did not have a constant speed at the upper end of the range? This is just a semantic complaint with the question but one that caused me to choose the wrong answer.

The take-away that I have is that you must assume the most ideal situation in all ways in order to calculate the maximum. In this case, that means disregarding the adverbial clause "depending on the terrain" and that "speed varies" to assume the upper limit of the speed capability. Is it standard to have to assume that the speed does not in fact vary?
Intern
Joined: 07 Aug 2011
Posts: 49
Concentration: Entrepreneurship, Finance
GPA: 3.87
Re: Cyclist Speed Varies, maximum distance travel in 7 hours?  [#permalink]

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11 Mar 2012, 15:33
I see what you mean and it hitched me up, too. I would think that since the problem suggests the the speed would vary with terrain - 14 mph traveling the optimal terrain, 6 mph traveling the least favorable terrain - then if the rider only covered optimal terrain then it would have resulted in an average of 14 mph for the entire seven hours.
Math Expert
Joined: 02 Sep 2009
Posts: 60515
Re: Cyclist Speed Varies, maximum distance travel in 7 hours?  [#permalink]

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12 Mar 2012, 00:16
gdh wrote:
Source: Knewton
A cyclist's speed varies, depending on the terrain, between 6.0 miles per hour and 14.0 miles per hour, inclusive. What is the maximum distance, in miles, that the cyclist could travel in 7 hours?

(A) 42
(B) 56
(C) 70
(D) 98
(E) 140

Here is my question, when a problem states that "speed varies," doesn't that mean that the biker did not have a constant speed at the upper end of the range? This is just a semantic complaint with the question but one that caused me to choose the wrong answer.

The take-away that I have is that you must assume the most ideal situation in all ways in order to calculate the maximum. In this case, that means disregarding the adverbial clause "depending on the terrain" and that "speed varies" to assume the upper limit of the speed capability. Is it standard to have to assume that the speed does not in fact vary?

While I agree that it's quite an odd way to make a simple question to look harder then it actually is, there is nothing mathematically wrong in it.

We are told that: generally a cyclist's speed varies, depending on the terrain, between 6.0 miles per hour and 14.0 miles per hour, inclusive. Is it possible the cyclist to travel with maximum speed for some time? Why not, if there is right terrain for that. So, if there is long enough terrain for the maximum speed of 14 mph then the maximum distance, in miles, that the cyclist could travel in 7 hours would be 7*14=98 miles.

Hope it helps.
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Re: Cyclist Speed Varies, maximum distance travel in 7 hours?   [#permalink] 12 Mar 2012, 00:16
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