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mrozelle5900
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Average speed question 08 Sep 2014, 11:49
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Peron makes a certain trip in their car. On the first leg they drive 40 miles per hour to the destination. On the second leg they turn around and drive the same route in 4 hours. How long do they spend on the first leg?
1. Average speed for the trip is 35 miles per hour.
2. The distance to the destination is 110 miles.

Thank you

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mikemcgarry
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Average speed question 08 Sep 2014, 12:04
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mrozelle5900
A person makes a certain trip in their car. On the first leg they drive 40 miles per hour to the destination. On the second leg they turn around and drive the same route in 4 hours. How long do they spend on the first leg?
1. Average speed for the trip is 35 miles per hour.
2. The distance to the destination is 110 miles.

Thank you
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Dear mrozelle5900,
I don't know the source of this question. When you post a question, please indicate the source, so I know who wrote the question. This question, at least in the phrasing presented here, has a subtle grammatical flaw -- using the plural pronoun "their" for the singular "person." In colloquial usage, this is a sloppy solution in order to avoid having to specify the gender of an unknown individual. This would not fly on the real GMAT, and all better GMAT sources would avoid this grammatical sloppiness.

Nevertheless, the mathematics of the question is sound. In fact, it's a very good math question. You understand why #2 is sufficient. Let's talk about #1.

Call the distance D.
First leg: D = (40 mph)*(T1)
Second leg: D = (V2)*T
Right now, that's three unknowns, and only two equations. With this prompt information only, we can't solve.

Now, toss in the average velocity information.
average V = (total distance)/(total time) = (2D)/(T1 + 4) = 35
Notice that if we substitute the "first leg" equation into the numerator, we get
2(40(T1))/((T1) + 4) = 35
We get a single equation that we can solve for (T1), the time on the first leg of the trip. Because this is GMAT DS, we can stop here: we have a single equation for a variable and we could solve it for that value. Done. This information is sufficient to find the value.

If this were a problem solving question, we would have to solve for (T1). That could also be a GMAT question, so I will show the solution:
Multiply by the denominator:
80(T1) = 35*((T1) + 4)
80(T1) = 35(T1) + 140
45(T1) = 140
T1 = 140/45 = 28/9 = 3 and (1/9) hours, or 3 hours and approximately 6-7 minutes.
The answer is an ugly decimal, but in the original question, that wasn't our concern at all, because answering a DS question sometimes has absolutely nothing to do with performing the calculation.

Does all this make sense?
Mike :-)