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

Question

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

(1) Harry’s average speed on his commute to work this Monday was 30 miles per hour.
(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.

Can someone please explain whether I have done it correctly or not?

Let d - distance between Harry's home and office
 r - Rate
 t - time

Considering Statement 1

Rate = Distance/Time
Distance = Rate * Time i.e D = 30 t. We can't calculate D unless we know t. Therefore, insufficient.

Considering Statement 2 on its own is clearly insufficient.

Considering both Statements together

If the speed remains 30mph then time will be 30 minutes   { Is his correct?}

Therefore, D = r*t = 30 * 30/60 = 15 miles. Therefore, C is the right answer.

nityamskhurana · Accepted Answer

Though a long method for DS, but solved it as

Distance between home and office = d

I) Speed s= 30mph.
No other info provided, hence Insufficient

II) Original Speed = s
 Original Time = t
 New Speed = 2s
 New Time = (t-0.25) [15 mins = 0.25hrs)

Distance is same, hence

s*t = 2s(t-0.25)
Solving results in t=0.5 hrs.

No info about speed hence, Insufficient.

I&II ) s= 30mph
 t= 0.5hrs
d= s*t => 15miles. Ans: C

Capricorn369 · Answer

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!

Chembeti · Answer

Agree with C.

As per the second statement, if he had traveled twice the speed, he would have saved half of the time. Combining this with the first statement, we come to know half of the time is 15 min and hence total or actual time would be 30min. Now we know speed and time and hence we can calculate distance.

BrentGMATPrepNow · Answer

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     
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

fskilnik · Answer

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

? = d\,\,\,\,\left

\left( 1 ight)\,\,\,V = 30\,\,{	ext{mph}}\,\,\,\left\{ \begin{gathered}
 \,{	ext{Take}}\,\,\,{	ext{T = }}\,\,{	ext{1}}\,\,{	ext{h}}\,\,\,\, \Rightarrow \,\,\,\,{	ext{?}}\,\,{	ext{ = }}\,\,{	ext{30}}\,\, \hfill \
 \,{	ext{Take}}\,\,\,{	ext{T = }}\,\,2\,\,{	ext{h}}\,\,\,\, \Rightarrow \,\,\,\,{	ext{?}}\,\,{	ext{ = }}\,\,60\,\,\, \hfill \ 
\end{gathered} ight.\,\,\,\left

\left( 2 ight)\,\,\,\,\frac{{d \cdot \boxed2}}{{V \cdot \boxed2}}\, - \frac{d}{{2V}}\,\,\,\,\,\mathop = \limits^{\left( * ight)} \,\,\,\,\frac{1}{4}\,\,\,\,\left \,\,\,\,\,\, \Rightarrow \,\,\,\,\underleftrightarrow {\frac{d}{{2V}} = \frac{1}{4}}\,\,\,\,\,\, \Rightarrow \,\,\,\,V = 2d\,\,\,\left( {**} ight)

\left( * ight)\,\,\,\frac{{\left }}{{\left }} = \left

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

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

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

Regards, 
fskilnik.

EncounterGMAT · Answer

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

sanjeevsinha082 · Answer

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.

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

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