M40-45

Question

George is at a location between his house and the concert hall. To reach the concert hall, he has two options, both taking the same amount of time: he can either walk directly there, or he can walk back to his house and then drive to the concert hall. If George drives 12 times as fast as he walks, what is the ratio of George's distance from his house to his distance from the concert hall?

A. \(1:11\)
B. \(11:12\)
C. \(11:13\)
D. \(13:11\)
E. \(11:1\)

A.  1:11 
B.  11:12 
C.  11:13 
D.  13:11 
E.  11:1

Bunuel · Answer

Official Solution:

George is at a location between his house and the concert hall. To reach the concert hall, he has two options, both taking the same amount of time: he can either walk directly there, or he can walk back to his house and then drive to the concert hall. If George drives 12 times as fast as he walks, what is the ratio of George's distance from his house to his distance from the concert hall?

A. \(1:11\)
B. \(11:12\)
C. \(11:13\)
D. \(13:11\)
E. \(11:1\)

A.  1:11 
B.  11:12 
C.  11:13 
D.  13:11 
E.  11:1

Let's assume George's distance from his house is  x , and his distance from the concert hall is  y . The question is asking us to find the ratio  \frac{x}{y} .
 
If we assume his walking speed is  v , then walking directly to the concert hall (the first option) would take a time of  \frac{y}{v} .
 
The second option, walking back to his house and then driving to the concert hall, would take a time of  \frac{x}{v} + \frac{x + y}{12v} .
 
Since both options take the same amount of time, we have  \frac{y}{v} = \frac{x}{v} + \frac{x + y}{12v} .
 
Multiplying everything by v to eliminate it, we get:  y = x + \frac{x + y}{12} . Simplifying this, we find  11y = 13x , leading to the ratio  \frac{x}{y} = \frac{11}{13} .

Answer: C

OmerKor · Answer

Hi Bunuel,

I just finished a test and got the question wrong.
I don't know if this is an official question but anyway I think it's better to write right ("Exactly") in the middle of his house and his concert hall.
Since it says "between" one might think (like me:/) that it could be anywhere in this area between the home and the city concert.
This is my recommendation.

Thanks (for your professionalism as you always handle issues in this forum)

Bunuel · Answer

You have missed the point! The problem asks for the ratio of George's distance from his house to the concert hall. If George were exactly in the middle, the ratio would be 1:1, making the question pointless. The whole essence of the question is that we don't know where between these points George is, and that's exactly what we're asked to find out!

gaurav51 · Answer

I think this is a  high-quality  question and I agree with explanation.

juansecalderon · Answer

I think this is a  high-quality  question and I agree with explanation. Great question & answer, although it can get confusing with the algebra. Are there alternative methods to approach this question?

Bunuel · Answer

This is a hard question, so it might take some time to work through it. Here is a thread with a couple of alternative solutions: https://gmatclub.com/forum/12-days-of-c ... 23299.html

Akshay1298 · Answer

Let the George's distance from his house be  A 
Let the George's distance from his concert hall be  B

Plug-in Option C - 11:13;

Assume that the total distance from home to concert hall is 2400m(2.4km),

then A = 1100m(1.1km) and B = 1300m(1.3 km)

Let us consider the walking speed - 10 m/s;

To calculate the time taken by walk for both A and B,
 
A's time = 1100/10 = 110 seconds and B's time = 1300/10 = 130 seconds.
So difference in time = 20 seconds.

Question task:  Once George reaches home, Will he drive for 2.4km in 20 seconds? Let's check!

George driving speed = 12 * walking speed;
 = 12 * 10 = 120 m/s;
So the time taken from home to concert hall = Total distance/ George's driving speed = 2400/120 = 20 seconds.

Answer - C

phmahi1997 · Answer

I like the solution - it’s helpful.

shisingh · Answer

My approach - Let total distance be D and George distance from concert be x so distance from house is D-X now walking speed is w 
so walk to concert is t1 = x/w
drive to concert is t2 =( D-X / W ) + (D /12W ) ( walk d-x to house at speed w and drive d for speed 12w )

solving t1 = t2 gives D-X/X = 11/13

Sushi_545 · Answer

good question i made mistake of understanding between as the mid point hence not ale to frame equation and thought if he is betwen how walking and going by car taking same time now i got this.

Adit_ · Answer

I like the solution - it’s helpful. I got this answer right by chance. My equation was like:
y/x=D-y/x+12D/x where D is total distance and x is the speed and I am equating the time. I got a 13 and 11 in my answer (albeit negative LOL) and hence got to my answer.
 Bunuel  would appreciate input!

Bunuel · Answer

Your issue is two things.

Parentheses: you wrote D - y/x, but it must be (D - y)/x. 
 The 12: if driving speed is 12x, driving time is D/(12x), not 12D/x.

Correct equation is y/x = (D - y)/x + D/(12x)

M40-45

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