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# A man travelled from one city to another. What is the distance between

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Joined: 02 Sep 2009
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A man travelled from one city to another. What is the distance between  [#permalink]

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05 Jul 2017, 00:48
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Difficulty:

45% (medium)

Question Stats:

61% (01:40) correct 39% (01:53) wrong based on 126 sessions

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A man travelled from one city to another. What is the distance between the two cities?

(1) He travelled the first 1/4 of his distance at a uniform speed of 15 miles per hour. Thereafter, he increased his speed to 20 miles per hour.
(2) The time for which he travelled at 20 miles per hour was 5 hours greater than the time for which he travelled at 15 miles per hour.

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Re: A man travelled from one city to another. What is the distance between  [#permalink]

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05 Jul 2017, 01:23
Bunuel wrote:
A man travelled from one city to another. What is the distance between the two cities?

(1) He travelled the first 1/4 of his distance at a uniform speed of 15 miles per hour. Thereafter, he increased his speed to 20 miles per hour.
(2) The time for which he travelled at 20 miles per hour was 5 hours greater than the time for which he travelled at 15 miles per hour.

Let the total distance be D and total time taken be t

(1) gives us
t1 = (x/4)/15
t2 = (3x/4)/20

And we know t1 + t2 = t
but two variables and one equation
Not sufficient

(2) gives us t2 = 5 + t1
Alone not sufficient as we don't know the individual time

Say if t1 was 1 hr then distance would be 135 miles
if t1 is 2 hr then distance would be 170 miles

On combining we can solve for x
(3x/4)/20 = 5 + (x/4)/15

Hence C
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Re: A man travelled from one city to another. What is the distance between  [#permalink]

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05 Jul 2017, 12:13
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(1) He traveled the first 1/4 of his distance at a uniform speed of 15 miles per hour. Thereafter, he increased his speed to 20 miles per hour.
clearly insufficient, as we only get a ratio of two distances traveled at a speed of 15m/h and 20m/h as 1:3, we cannot find the actual distance

(2) The time for which he traveled at 20 miles per hour was 5 hours greater than the time for which he traveled at 15 miles per hour.
clearly insufficient, as only the difference between the two times is given and this condition can be satisfied by many sets of values(1,6 or 2,7 or 3,8 etc.)

Combining the two statements, we can calculate the distance between the two cities by considering the total distance to be x and forming equations as below:
((3x/4)/20) - ((x/4)/15) = 5

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Re: A man travelled from one city to another. What is the distance between  [#permalink]

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15 Feb 2019, 11:21
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Re: A man travelled from one city to another. What is the distance between   [#permalink] 15 Feb 2019, 11:21
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