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I know this is slightly off-topic here, but it's really bothering me.

My class was given the following immensely simple problem today:

A bird flies due south at a constant speed of $45\frac{\text{km}}{\text{h}}$ for 10 minutes. How far does it travel in the 10 minutes?

One of my classmates is claiming that the answer to this should be in units of velocity ($\frac{7.5\text{ km}}{10\text{ min}}$). Everyone else in the school has been trying unsuccessfully that the answer should be in units of distance (7.5 km).

We've told him repeatedly that the direct question is "how far does it travel," not "how fast does it travel." His response, as far as I can tell, is along the lines of "If it did not say 'in the 10 minutes' at the end of the question (as the 10 minutes were already specified), yes, the answer would be in units of distance; however, it's specifically saying 'in ten minutes,' so it's clearly asking for you to find the velocity, not the distance."

Which side is correct here? Since most of you will answer that the question is asking for distance, do you have any ideas how I could get him to believe that?

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Yes it should be 7.5km. Because you are doing 45 km/hr x 1/6 hr. when you multiply, the units cancels so, you get 45/6 km – Lost1 Apr 10 '13 at 22:29

I agree the answer should be in distance. Without the $10$ minutes, you couldn't get a distance. Your friend's logic would also imply that $\frac{7.5\text{ km}}{10\text{ min}}\neq\frac{15\text{ km}}{20\text{ min}}$

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I guess because of the language, he is trying to interpret the question as "How far per 10 minutes can the bird travel?" If he is really stubborn about this, you might just have to let him see the red mark that your teacher puts on his answer and be done with it. Otherwise, if you think there is hope, you might point out that no one ever expresses velocities in km/10min or miles/2hrs or whatever. Problems like this are not supposed to be an exercise in linguistic analysis, but questions leading to somewhat real world answers. You're right, of course. Good luck to you and to your friend.

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Even if the question were worded as "How far per...," the answer would still be 7.5 km. And trust me, we're way past the red mark point. – Tortoise Apr 11 '13 at 1:43

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