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Mary goes from her house to the library at a constant speed rate of 40

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Mary goes from her house to the library at a constant speed rate of 40  [#permalink]

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New post Updated on: 22 Feb 2019, 23:15
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Mary goes from her house to the library at a constant speed rate of 40 miles per hour and come back from the library to her house at a constant rate of 45 miles per hour along the same route. What is the distance of the route?

(1) The difference between the round trip’s times taken is 2 minutes
(2) The total amount of minutes for the round trip taken is 34 minutes

Originally posted by indu1954 on 22 Feb 2019, 12:51.
Last edited by Bunuel on 22 Feb 2019, 23:15, edited 2 times in total.
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Re: Mary goes from her house to the library at a constant speed rate of 40  [#permalink]

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New post 22 Feb 2019, 23:37
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OA:D

Let the distance between Mary's Home and Library be \(x\).
\(Average Speed_{(Home ->Library)} = 40\) miles per hour
\(Average Speed_{(Library ->Home)} = 45\) miles per hour

(1) The difference between the round trip’s times taken is 2 minutes

i.e \(\frac{x}{Average Speed_{(Home ->Library)}} - \frac{x}{Average Speed_{(Library ->Home)}}=2\)

\(\frac{x}{40} - \frac{x}{45}=2\)

We can easily find out the value of x, So Statement 1 alone is sufficient.

(2) The total amount of minutes for the round trip taken is 34 minutes

i.e \(\frac{x}{Average Speed_{(Home ->Library)}} + \frac{x}{Average Speed_{(Library ->Home)}}=34\)

\(\frac{x}{40} + \frac{x}{45}=34\)

We can easily find out the value of \(x\), So Statement 2 alone is sufficient.
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Re: Mary goes from her house to the library at a constant speed rate of 40  [#permalink]

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New post 13 Jan 2020, 01:04
Mary goes from her house to the library at a constant speed rate of 40 miles per hour and come back from the library to her house at a constant rate of 45 miles per hour along the same route. What is the distance of the route?

(1) The difference between the round trip’s times taken is 2 minutes
(2) The total amount of minutes for the round trip taken is 34 minutes

Soln: Lets the distance from Home to library be d

Speed * time= distance Hence 40*t1=d
Similarly for library to home 45*t2=d
as distance is same we can equate both i.e 40*t1=45*t2

(Rem- speed is given to us in miles/hour, where as if we see in both statements time is given in mins)
so its better to convert into mins

40/60*t1=45/60*t2
simplifying ,2/3t1=3/4t2

Now lets check each statement

(1) The difference between the round trip’s times taken is 2 minutes

t1-t2=2mins
hence t1= t2+2
we can replace this in equation 2/3t1=3/4t2 and get the time and hence the distance.

So st 1 is sufficient

St 2 The total amount of minutes for the round trip taken is 34 minutes
Here we are given t1+t2=34
t1=34-t2
Again can replace this in equation 2/3t@1=3/4t2 and get t1 and t2 and also cal distance/

St 2 is also sufficient.

Hence ans is D

Bunuel, VeritasKarishma Please suggest if my method is correct. It took more than 2 mins to solve this question.
Please guide if any other shorter method or logic to solve this question
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Re: Mary goes from her house to the library at a constant speed rate of 40  [#permalink]

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New post 13 Jan 2020, 22:18
1
indu1954 wrote:
Mary goes from her house to the library at a constant speed rate of 40 miles per hour and come back from the library to her house at a constant rate of 45 miles per hour along the same route. What is the distance of the route?

(1) The difference between the round trip’s times taken is 2 minutes
(2) The total amount of minutes for the round trip taken is 34 minutes


The speeds of the two journeys are in the ratio 40:45 = 8:9

So time taken for the two journeys are in the inverse ratio = 9:8

(1) The difference between the round trip’s times taken is 2 minutes

The diff of 1 on ratio scale is actually 2 mins. So multiplier is 2 and time taken at 40 miles/hr is 9*2 = 18 mins. Distance = 40*18/60 = 12 miles

(2) The total amount of minutes for the round trip taken is 34 minutes

The total time taken on ratio scale is 9+8 = 17. Actual total time = 34 mins. So multiplier is 2 and time taken at 40 miles/hr = 9*2 = 18 mins. Distance = 40*18/60 = 12 miles

Answer (D)

Note that all this needn't be calculated. Just knowing the ratio of the speeds gives us the ratio of time taken and if we have actual value for something related to time taken, we can find the actual time taken. Using actual speeds, we can find the distance.
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Re: Mary goes from her house to the library at a constant speed rate of 40  [#permalink]

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New post 13 Jan 2020, 22:19
1
Win2020 wrote:
Mary goes from her house to the library at a constant speed rate of 40 miles per hour and come back from the library to her house at a constant rate of 45 miles per hour along the same route. What is the distance of the route?

(1) The difference between the round trip’s times taken is 2 minutes
(2) The total amount of minutes for the round trip taken is 34 minutes

Soln: Lets the distance from Home to library be d

Speed * time= distance Hence 40*t1=d
Similarly for library to home 45*t2=d
as distance is same we can equate both i.e 40*t1=45*t2

(Rem- speed is given to us in miles/hour, where as if we see in both statements time is given in mins)
so its better to convert into mins

40/60*t1=45/60*t2
simplifying ,2/3t1=3/4t2

Now lets check each statement

(1) The difference between the round trip’s times taken is 2 minutes

t1-t2=2mins
hence t1= t2+2
we can replace this in equation 2/3t1=3/4t2 and get the time and hence the distance.

So st 1 is sufficient

St 2 The total amount of minutes for the round trip taken is 34 minutes
Here we are given t1+t2=34
t1=34-t2
Again can replace this in equation 2/3t@1=3/4t2 and get t1 and t2 and also cal distance/

St 2 is also sufficient.

Hence ans is D

Bunuel, VeritasKarishma Please suggest if my method is correct. It took more than 2 mins to solve this question.
Please guide if any other shorter method or logic to solve this question


Yes, your method is correct too but using ratios helps avoid variables.
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Re: Mary goes from her house to the library at a constant speed rate of 40  [#permalink]

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New post 13 Jan 2020, 22:28
VeritasKarishma wrote:
indu1954 wrote:
Mary goes from her house to the library at a constant speed rate of 40 miles per hour and come back from the library to her house at a constant rate of 45 miles per hour along the same route. What is the distance of the route?

(1) The difference between the round trip’s times taken is 2 minutes
(2) The total amount of minutes for the round trip taken is 34 minutes


The speeds of the two journeys are in the ratio 40:45 = 8:9

So time taken for the two journeys are in the inverse ratio = 9:8

(1) The difference between the round trip’s times taken is 2 minutes

The diff of 1 on ratio scale is actually 2 mins. So multiplier is 2 and time taken at 40 miles/hr is 9*2 = 18 mins. Distance = 40*18/60 = 12 miles

(2) The total amount of minutes for the round trip taken is 34 minutes

The total time taken on ratio scale is 9+8 = 17. Actual total time = 34 mins. So multiplier is 2 and time taken at 40 miles/hr = 9*2 = 18 mins. Distance = 40*18/60 = 12 miles

Answer (D)

Note that all this needn't be calculated. Just knowing the ratio of the speeds gives us the ratio of time taken and if we have actual value for something related to time taken, we can find the actual time taken. Using actual speeds, we can find the distance.


Thank you @VeritaKarishma, Really helpful method to solve.
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Re: Mary goes from her house to the library at a constant speed rate of 40  [#permalink]

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New post 14 Jan 2020, 00:59
Lets the distance be D.
Now D=RT or
D=40*T1
D= 45*T2
And as distance is same we can equate both
i.e 40*T1=45*T2

Converting into minutes we get
40/60*T1=45/60*T2
2/3 T1=3/4 T2

Statement 1 says difference between the round trip’s times taken is 2 minutes
or T1-T2=2mins
hence T1= T2+2
we can replace this in equation 2/3T1=3/4T2 to get the time and hence the distance.
So statement 1 alone is sufficient.
Keep AD.

Statement 2 says that the total amount of minutes for the round trip taken is 34 minutes
Here we are given T1+T2=34
T1=34-T2
Again we can replace this in equation 2/3T1=3/4T2 to get the time and hence the distance.
ie Statement 2 alone is also sufficient.

Hence answer is option D.
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Re: Mary goes from her house to the library at a constant speed rate of 40   [#permalink] 14 Jan 2020, 00:59
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