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

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What is the distance between Harry s home and his office?  [#permalink]

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10 Nov 2011, 15:50
2
12
00:00

Difficulty:

15% (low)

Question Stats:

78% (01:22) correct 22% (01:13) wrong based on 665 sessions

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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.

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Re: Distance between office and work - Ivy Q17  [#permalink]

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10 Nov 2011, 17:09
enigma123 wrote:
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.

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.

Cheers!
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Re: What is the distance between Harry s home and his office?  [#permalink]

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08 Feb 2012, 05:45
1
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.
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Re: What is the distance between Harry s home and his office?  [#permalink]

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15 Feb 2014, 09:03
3
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
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Re: What is the distance between Harry s home and his office?  [#permalink]

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03 Apr 2018, 09:08
Top Contributor
enigma123 wrote:
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.

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,

(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

Cheers,
Brent
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Re: What is the distance between Harry s home and his office?  [#permalink]

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07 Sep 2018, 07:22
enigma123 wrote:
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.

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.
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Re: What is the distance between Harry s home and his office?  [#permalink]

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17 Nov 2018, 09:34
Can someone explain it in a matrix? Thanks a lot in advance
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Re: What is the distance between Harry s home and his office?   [#permalink] 17 Nov 2018, 09:34
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