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# John went up a certain hill at the rate of one and a half kilometers p

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Intern
Joined: 03 Mar 2016
Posts: 4
John went up a certain hill at the rate of one and a half kilometers p  [#permalink]

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Updated on: 10 Mar 2016, 22:25
1
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Difficulty:

35% (medium)

Question Stats:

69% (01:48) correct 31% (02:28) wrong based on 85 sessions

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John went up a certain hill at the rate of one and a half kilometers per hour and came down at the rate of four and a half kilometers per hour, so that it took just four hours to make the double journey. How far was it to the top of the hill ?
A. 3 km
B. 6 km
C. 4.5 km
D.9 km
E. none of the above

Originally posted by rubyrose on 10 Mar 2016, 17:42.
Last edited by rubyrose on 10 Mar 2016, 22:25, edited 1 time in total.
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Joined: 27 Nov 2015
Posts: 1
Location: India
GPA: 3.83
Re: John went up a certain hill at the rate of one and a half kilometers p  [#permalink]

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10 Mar 2016, 18:07
I didn't understand how we got the answer as: 9km. In my view, it should have been 4.5km.
Lets see the solution below -

Assume the distance to the top of the hill (1 way) as: x
Now, speed=distance/time => time=distance/speed
So, for the first half of the journey, he traveled uphill at 1.5km/hr, so the time taken for the first leg of the journey is: x/1.5.
For the second half, he traveled downhill at 4.5km/hr, so the time taken for the second leg of the journey is: x/4.5

Now, the total time for the trip is given as 4 hrs.

Equating, (x/1.5)+(x/4.5)=4 => (3x+x)/4.5=4 => x=4.5 km
So, the distance one side is = 4.5 km.

The OA mentioned is 9km, which is exactly double of this distance, i.e., the total distance traveled during both legs of the journey, but the question only asked for the distance till the top of the hill, i.e., one way, so the answer should be 4.5km

Can someone assist me in understanding where am I wrong here?
Math Expert
Joined: 02 Aug 2009
Posts: 7025
Re: John went up a certain hill at the rate of one and a half kilometers p  [#permalink]

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10 Mar 2016, 19:24
sunnyshukla2008 wrote:
I didn't understand how we got the answer as: 9km. In my view, it should have been 4.5km.
Lets see the solution below -

Assume the distance to the top of the hill (1 way) as: x
Now, speed=distance/time => time=distance/speed
So, for the first half of the journey, he traveled uphill at 1.5km/hr, so the time taken for the first leg of the journey is: x/1.5.
For the second half, he traveled downhill at 4.5km/hr, so the time taken for the second leg of the journey is: x/4.5

Now, the total time for the trip is given as 4 hrs.

Equating, (x/1.5)+(x/4.5)=4 => (3x+x)/4.5=4 => x=4.5 km
So, the distance one side is = 4.5 km.

The OA mentioned is 9km, which is exactly double of this distance, i.e., the total distance traveled during both legs of the journey, but the question only asked for the distance till the top of the hill, i.e., one way, so the answer should be 4.5km

Can someone assist me in understanding where am I wrong here?

You are correct, the distance is 4.5 km one way..
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Intern
Joined: 03 Mar 2016
Posts: 4
Re: John went up a certain hill at the rate of one and a half kilometers p  [#permalink]

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10 Mar 2016, 22:26
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Re: John went up a certain hill at the rate of one and a half kilometers p  [#permalink]

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28 Jul 2018, 02:03
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: John went up a certain hill at the rate of one and a half kilometers p &nbs [#permalink] 28 Jul 2018, 02:03
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