What is the distance between Harry s home and his office?

Let d = distance between Harry’s home and his office

Target question: What is the distance between Harry’s home and his office?

Statement 1: Harry’s average speed on his commute to work this Monday was 30 miles per hour.
To determine the distance (d), we need the travel time.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: If Harry’s average speed on his commute to work this Monday had been twice as fast, his trip would have been 15 minutes shorter.
Travel time = (distance)/(speed)
Let v = Monday's speed,

Start with a word equation:
(Monday's travel time) = (travel time at twice Monday's speed) + 15 minutes
Or..., (Monday's travel time) = (travel time at twice Monday's speed) + 0.25 hours
So, we can write d/v = d/2v + 0.25
Multiply both sides by 2v to get: 2d = d + 0.5v
Simplify: d = 0.5v
Divide both sides by v to get: d/v = 0.5
NOTE: distance/speed = time [in other words, time = d/v]
So, the Monday's travel time = 0.5 hours
So, statement 2 allows us to determine Monday's travel time, but we don't know Harry's speed.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that Harry's speed was 30 mph
Statement 2 tells us that Harry drove for 0.5 hours
Distance = (speed)(time)
So, distance = (30)(0.5) = 15 miles
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

If the speed remains 30mph then time will be 30 minutes - Absolutely Correct!!!!
D = r*t = 30 * 30/60 = 15 miles. - Method of solving this problem is correct.

C is indeed the answer.
Cheers!

Excellent opportunity to practice UNITS CONTROL and BIFURCATION, two of our most powerful tools!

\(? = d\,\,\,\,\left[ {{\text{miles}}} \right]\)

\(\left( 1 \right)\,\,\,V = 30\,\,{\text{mph}}\,\,\,\left\{ \begin{gathered}\\
\,{\text{Take}}\,\,\,{\text{T = }}\,\,{\text{1}}\,\,{\text{h}}\,\,\,\, \Rightarrow \,\,\,\,{\text{?}}\,\,{\text{ = }}\,\,{\text{30}}\,\, \hfill \\\\
\,{\text{Take}}\,\,\,{\text{T = }}\,\,2\,\,{\text{h}}\,\,\,\, \Rightarrow \,\,\,\,{\text{?}}\,\,{\text{ = }}\,\,60\,\,\, \hfill \\ \\
\end{gathered} \right.\,\,\,\left[ {{\text{miles}}} \right]\)

\(\left( 2 \right)\,\,\,\,\frac{{d \cdot \boxed2}}{{V \cdot \boxed2}}\, - \frac{d}{{2V}}\,\,\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,\,\frac{1}{4}\,\,\,\,\left[ {\text{h}} \right]\,\,\,\,\,\, \Rightarrow \,\,\,\,\underleftrightarrow {\frac{d}{{2V}} = \frac{1}{4}}\,\,\,\,\,\, \Rightarrow \,\,\,\,V = 2d\,\,\,\left( {**} \right)\)

\(\left( * \right)\,\,\,\frac{{\left[ {{\text{miles}}} \right]}}{{\left[ {{\text{mph}}} \right]}} = \left[ {\text{h}} \right]\)

\(\left\{ \begin{gathered}\\
\,{\text{Take}}\,\,\,V = 2\,{\text{mph}}\,\,\,\,\mathop \Rightarrow \limits^{\left( {**} \right)} \,\,\,\,\,{\text{d = }}\,\,{\text{1}}\,\,{\text{mile}}\,\,\,\,\left( {T = 0.5\,\,{\text{h}}} \right)\,\,\,\,::\,\,\,\,{\text{viable!}}\,\,\,\,\, \hfill \\\\
\,\,{\text{Take}}\,\,\,V = 4\,{\text{mph}}\,\,\,\,\mathop \Rightarrow \limits^{\left( {**} \right)} \,\,\,\,\,{\text{d = }}\,\,{\text{2}}\,\,{\text{miles}}\,\,\,\,\left( {T = 0.5\,\,{\text{h}}} \right)\,\,\,\,::\,\,\,\,{\text{viable!}}\,\,\,\, \hfill \\ \\
\end{gathered} \right.\)

\(\left( {1 + 2} \right)\,\,\,\,V = 30\,{\text{mph}}\,\,\,\,\mathop \Rightarrow \limits^{\left( {**} \right)} \,\,\,\,\,\boxed{{\text{d = }}\,\,{\text{15}}\,\,{\text{miles}}}\,\,\,\,\,\,\)


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

Regards,
fskilnik.

Can someone explain it in a matrix? Thanks a lot in advance

Distance = Rate × Time, or D = RT.
(1) INSUFFICIENT: This statement tells us Harry‟s rate, 30 mph. This is not enough
to calculate the distance from his home to his office, since we don‟t know anything
about the time required for his commute.
D = RT = (30 mph) (T)
D cannot be calculated because T is unknown.
(2) INSUFFICIENT: If Harry had traveled twice as fast, he would have gotten to
work in half the time, which according to this statement would have saved him 15
minutes. Therefore, his actual commute took 30 minutes. So we learn his commute
time from this statement, but don‟t know anything about his actual speed.
D = RT = (R) (1/2 hour)
D cannot be calculated because R is unknown.
(1) AND (2) SUFFICIENT: From statement (1) we learned that Harry‟s rate was 30
mph. From Statement (2) we learned that Harry‟s commute time was 30 minutes.
Therefore, we can use the rate formula to determine the distance Harry traveled.
D = RT = (30 mph) (1/2 hour) = 15 miles
The correct answer is C.

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.