Speed Problems: Speed Definition

Judy ran along the fence that surrounds her house. The fence forms a rectangle whose dimensions are $$20\times30$$ meters. Beginning from a vertex of the rectangle, Judy started running along one of the long sides and stopped when she had completed running along 7 sides. This jog took her 30 seconds. What was Judy's speed in meters per second?

Incorrect. You may have reached this answer by disregarding the distance Judy traveled _around_ the rectangle and assuming that the relevant distance is the _shortest_ distance between the starting point and the ending point of the run. Is that the case?

When calculating the speed, you should consider the overall distance that Judy covered. This may not be the same as the distance between where she started and where she stopped. In the GMAT, your ability to extract relevant data from the question without getting lost is far more important, and far more influential on your score, than remembering formulas.

Well then, you should have noticed that this answer can be _eliminated_ by a rough _estimation_ of the correct answer. Judy's speed must exceed 1 meter per second since she had run more meters than the time measured in seconds.

Incorrect. Did you assume that the relevant distance was the total length of the three last sides along which Judy ran?

Okay, then you must have made some other error in your calculation.

That's only part of the distance covered by Judy in her run. You should have considered the entire distance. In the GMAT, your ability to extract relevant data from the question without getting lost is far more important, and far more influential on your score, than remembering formulas.

Incorrect. Judy ran along 7 _sides_ of the rectangle; she didn't run around the rectangle 7 times. Don't be hasty. Read the question carefully, and be wary of making your own assumptions.

Incorrect. In the GMAT, few questions are really just about a mathematical formula. The main issue here is handling information and paying attention to details. If Judy had run along 8 full sides, she would have completed two full rounds. Her actual path falls short of two full rounds by one side, the side _before_ the completion of the last round. The missing side must be a _short_ side since it must lead her to the starting point, which is the beginning of a long side. The relevant distance is therefore the length of two full rounds minus a short side. Go on and finish the job!

Correct. As you've probably noticed, a speed question can really be about handling information. If Judy had run along 8 full sides, she would have completed two full rounds. Her actual path falls short of two full rounds by one side, the side _before_ the completion of the last round. The missing side must be a _short_ side since it must lead her to the starting point, which is the beginning of a long side. Therefore, the total distance is 180 meters: two full rounds (100 meters each) minus one short side (20 meters). | | SPEED | TIME | DISTANCE | |-------|-------|------------|------------| | Judy | $$\color{red}{?}$$ | $$30$$ seconds | $$180$$ meters | Finally, calculate the speed by dividing distance by time: >$$\displaystyle \text{Speed} = \frac{180\ \text{meters}}{30\ \text{seconds}} = 6\ \text{meters per second}$$

$$ \frac{2}{3}$$

$$ \frac{8}{3}$$

$$ \frac{17}{3} $$

$$6 $$

$$23 \frac{1}{3} $$

Yes, I used 20 meters as the distance for calculating the speed.

No, I did not assume that.

Yes, that was my assumption.

No, I don't see the point in assuming that.