How many hours did it take Dale to drive from A-town to B-to

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How many hours did it take Dale to drive from A-town to B-town?

(1) If Dale's average speed for the trip had been three times as fast, the trip would have taken 2 hours.

(2) The distance from A-town to B-town is 100 miles.

OA A

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by GMATGuruNY » Fri Sep 07, 2018 4:41 am

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BTGmoderatorDC wrote:How many hours did it take Dale to drive from A-town to B-town?

(1) If Dale's average speed for the trip had been three times as fast, the trip would have taken 2 hours.

(2) The distance from A-town to B-town is 100 miles.
Statement 1:
Time and rate have a RECIPROCAL relationship.
3 TIMES AS FAST implies 1/3 THE TIME.
Thus, the 2 hours that would be spent traveling 3 times as fast must be equal to 1/3 the actual time:
2 = (1/3)t
t = 6 hours.
SUFFICIENT.

Statement 2:
Here, the time can be any nonnegative value.
INSUFFICIENT.

The correct answer is A.
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by fskilnik@GMATH » Fri Sep 07, 2018 6:57 am

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BTGmoderatorDC wrote:How many hours did it take Dale to drive from A-town to B-town?

(1) If Dale's average speed for the trip had been three times as fast, the trip would have taken 2 hours.
(2) The distance from A-town to B-town is 100 miles.

Source: Magoosh
Excellent opportunity to practice UNITS CONTROL and BIFURCATION, two of our most powerful tools!
\[? = {T_{\,A\, \to \,B}}\,\,\,\left[ {\text{h}} \right]\,\,\,\,\mathop = \limits^{{\text{UNITS}}\,\,\,{\text{CONTROL}}\,\,\left( * \right)} \,\,\,\,\,\,\boxed{\frac{{d\,\,\,{\text{miles}}}}{{V\,\,\frac{{{\text{miles}}}}{{\text{h}}}}} = ?}\,\,\,\,\,\,\,\,\,\,\,\,\left[ {\left( * \right)\,\,\,\frac{{{\text{miles}}}}{{\,\,\,\,\frac{{{\text{miles}}}}{{\text{h}}}\,\,\,}} = {\text{h}}\,} \right]\]
\[\left( 1 \right)\,\,\,2\,{\text{h}}\,\,\left( {\frac{{3V\,\,{\text{miles}}}}{{1\,\,\,{\text{h}}}}} \right)\,\,\, = \,\,\,6V\,\,{\text{ = }}\,\,\,{\text{d }}\,\,\,\left[ {{\text{miles}}} \right]\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,?\,\, = \frac{{6V}}{V} = 6\,\,\,\left[ {\text{h}} \right]\,\,\]
\[\left( 2 \right)\,\,\,d = 100\,\,{\text{miles}}\,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,\,{\text{V = }}\,\,{\text{100}}\,\,{\text{mph}}\,\,\,\, \Rightarrow \,\,\,\,{\text{?}}\,\,{\text{ = }}\,\,{\text{1}}\,\, \hfill \\
\,{\text{Take}}\,\,\,{\text{V = }}\,\,5{\text{0}}\,\,{\text{mph}}\,\,\,\, \Rightarrow \,\,\,\,{\text{?}}\,\,{\text{ = }}\,\,2\,\, \ne 1\,\,\, \hfill \\
\end{gathered} \right.\,\,\,\left[ {\text{h}} \right]\]

This solution follows the notations and rationale taught in the GMATH method.

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