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How many miles long is the route from Houghton to Callahan?

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How many miles long is the route from Houghton to Callahan?  [#permalink]

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New post Updated on: 21 Jul 2013, 09:08
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How many miles long is the route from Houghton to Callahan?

(1) It will take 1 hour less time to travel the entire route at an average rate of 55 miles per hour than at an average rate of 50 miles per hour.
(2) It will take 11 hours to travel the first half of the route at an average rate of 25 miles per hour

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Originally posted by fiendex on 06 Feb 2012, 08:55.
Last edited by Bunuel on 21 Jul 2013, 09:08, edited 1 time in total.
Edited the tags.
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Re: How many miles long is the route from Houghton to Callahan?  [#permalink]

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New post 06 Feb 2012, 09:17
1
Statement 1.

50 = D/(T+1)
55= D/T

Ds are equal so isolate D.
50(T+1) = D
55(T) =D
Both equation equal to D just need to solve for T
55 T -50T = 50 ==> 10 = T.
R * T = D
D = 550

Statement 2:
11 *25 = 225
1/2 D = 225.
D = 550
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Re: How many miles long is the route from Houghton to Callahan?  [#permalink]

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New post 01 Aug 2013, 16:18
How many miles long is the route from Houghton to Callahan?


(1) It will take 1 hour less time to travel the entire route at an average rate of 55 miles per hour than at an average rate of 50 miles per hour.

t-1 = d/55
t = d/50

(d/50) - 1 = (d/55)
55d/50 - 55 = d
11d/10 - 55 = d
11d/10 = d + 55
11d = 10d + 550
d = 550
SUFFICIENT

(2) It will take 11 hours to travel the first half of the route at an average rate of 25 miles per hour
d = r*t
d = 25*11
d = 275

If one half of the distance is covered in 11 hours at an average of 25 miles/hour, that means the first half of the distance = 275 miles.
SUFFICIENT

(D)
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Re: How many miles long is the route from Houghton to Callahan?  [#permalink]

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New post 10 May 2015, 23:45
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Hi Guys,

It's a DS question and we don't need to calculate the actual distance between Houghton and Callahan; just the analysis that the information provided in the statements is sufficient is enough to answer our question.

Analyze the Given Info:
The question asks us if the information provided in the statements is sufficient to calculate the distance between two places. We know that Distance = Speed * Time. So, if we are given the values of speed & time taken, we can find the distance between the places. Let's evaluate the information given in the statements to see if it provides us the required information.

Analyze statement-I independently
St-I gives us two scenarios of speed & time taken to cover the same distance. Let's write equations for both the scenarios:

a. Time taken to cover the distance at a speed of \(55 \frac{miles}{hour} = \frac{D}{55}\) assuming the distance between Houghton and Callahan to be D.

b. Time taken to cover the same distance at a speed of \(50 \frac{miles}{hour} = \frac{D}{50}\).

Since we know that the difference between the time taken is 1 hour, we can write \(\frac{D}{50} - \frac{D}{55} = 1\).
From this equation, we can easily find out a unique value of D. Hence, statement-I is sufficient to answer the question.

Analyze statement-II independently
St-II tells us that it takes 11 hours to cover half the distance at a speed of 25 miles/hour. So, we can write \(\frac{D}{2} = 11* 25\).
Again, this equation would give us a unique value of D. Hence, statement-II alone is sufficient to answer the question.

It's important to remember that DS question does not ask us to find the actual value of the unknown. Once we deduce that the information provided in the statements is sufficient to find out a unique value of the unknown, we should not be doing further calculations to save our time.

Regards
Harsh
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How many miles long is the route from Houghton to Callahan?  [#permalink]

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New post 17 Feb 2016, 10:13
Statement 1: Ratio of average rates for same distance: 11:10, therefore ratio of time taken will be 10:11. As it is also given that time difference is 1 hr, actual time taken is 10 hrs at 55 mph and 11 hrs at 50 mph. We can calculate distance, thereby making statement sufficient.

Statement 2: Sufficient as both rate and time are provided, we can calculate distance.

Answer: D
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Re: How many miles long is the route from Houghton to Callahan?  [#permalink]

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New post 17 Apr 2018, 06:30
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).

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Re: How many miles long is the route from Houghton to Callahan? &nbs [#permalink] 17 Apr 2018, 06:30
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