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While driving on a highway, Harry and Ron crossed checkpoint P at 9 am

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While driving on a highway, Harry and Ron crossed checkpoint P at 9 am  [#permalink]

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New post Updated on: 12 Aug 2018, 23:59
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e-GMAT Question of the Week #4


While driving on a highway, Harry and Ron crossed checkpoint P at 9 am and 10 am, at individual speeds of 30 mph and 40 mph respectively. Professor Snape started cycling in the same direction as Harry and Ron, from point Q at 8 am at 15 mph. If Harry and Ron met each other at Q, then at what distance from Q Ron met Professor?

    A. 40
    B. 60
    C. 80
    D. 120
    E. 160



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Originally posted by EgmatQuantExpert on 22 Jun 2018, 07:25.
Last edited by EgmatQuantExpert on 12 Aug 2018, 23:59, edited 3 times in total.
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Re: While driving on a highway, Harry and Ron crossed checkpoint P at 9 am  [#permalink]

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New post 22 Jun 2018, 07:51
EgmatQuantExpert wrote:
e-GMAT Question of the Week #4


While driving on a highway, Harry and Ron crossed checkpoint P at 9 am and 10 am, at individual speeds of 30 mph and 40 mph respectively. Professor Snape started cycling in the same direction as Harry and Ron, from point Q at 8 am at 15 mph. If Harry and Ron met each other at Q, then at what distance from Q Ron met Professor?

    A. 40
    B. 60
    C. 80
    D. 120
    E. 160


Let us also work on the checkpoints..
When Ron starts at 10am, Harry has travelled for an hour is therefore 30 miles ahead and that point is Q..
Ron covers 40-30=10 miles in each hour so he will cover 30 miles in 30/10=3hours..
So Ron reaches Q at 10+3 or 1pm...
And by 1 pm, prof has travelled for 1pm-8am or 5hrs..

In 5hrs, prof has traveled 5*15=75 miles..
To cover this distance Ron requires 75/(40-15)=3hrs
In these 3 hours Ron has travelled 3*40=120 miles
So Ans 120

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Re: While driving on a highway, Harry and Ron crossed checkpoint P at 9 am  [#permalink]

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New post 22 Jun 2018, 10:16
EgmatQuantExpert wrote:
e-GMAT Question of the Week #4


While driving on a highway, Harry and Ron crossed checkpoint P at 9 am and 10 am, at individual speeds of 30 mph and 40 mph respectively. Professor Snape started cycling in the same direction as Harry and Ron, from point Q at 8 am at 15 mph. If Harry and Ron met each other at Q, then at what distance from Q Ron met Professor?

    A. 40
    B. 60
    C. 80
    D. 120
    E. 160


Harry and Ron both met at point Q, means that they travelled the same distance D.
Harry D = Speed x (time + 1) ..... since harry took 1 hour more than Ron to cover same distance
Ron D = Speed x Time

Equating both distances, 30t+30 = 40t
So, t = 3 hours.

Ron took off 2 hours after Snape and reached at Q, therefore, Ron took 5 hours to reach Q
therefore, in 5 hours, snape covered 5 x 15 = 75 miles

use relative speed for finding relative time
so, Ron require relative time T to cover these 75 miles, i.e. 75/(40-15)..... since both travelling in same direction

T = 3 hours,
in these 3 hours , Ron would have covered, 3 x 40 = 120 miles !
Hence, Ron met Snape at 120 miles.
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Re: While driving on a highway, Harry and Ron crossed checkpoint P at 9 am  [#permalink]

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New post 22 Jun 2018, 12:34
1
Lets consider the positions of each entity at 10 am.

Ron 10 am is at point P

Harry 10 am is at a distance of 30 miles from point P, (since speed of harry is 30mph & he was at point P @9 am)

Professor Snape 10 am has traveled for 2 hours at a speed of 15 mph, hence he is at 30 miles from point Q.



Now Ron & Harry meet at point Q, hence they together have to cover a distance of 30 miles between them.

Relative speed of Ron & Harry = 40 - 30 = 10 mph,

Hence they will take 3 hours to cover the 30 miles between them & meet each other at point Q.

Therefore they meet at point Q at 1 pm.



@1 pm Professor Snape has traveled for an additional 3 hours at speed 15 mph, hence he has traveled for 5 hours & is at 75 miles from point Q.

Now relative distance between Ron & Professor Snape is 75 miles

The relative speed at which they travel is = 40 - 15 = 25 mph

Ron will meet Professor Snape in 75/25 = 3 hours



In these 3 hours, Ron has traveled a distance of 3*40 = 120 miles

Hence Ron meets Professor Snape at a distance of 120 miles from point Q.

Answer D.


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While driving on a highway, Harry and Ron crossed checkpoint P at 9 am  [#permalink]

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New post 25 Jun 2018, 23:22

Solution



Given:
    • While driving on a highway, Harry and Ron crossed checkpoint P at 9 am and 10 am, at individual speeds of 30 mph and 40 mph respectively
    • Professor Snape started cycling in the same direction as Harry and Ron, from point Q at 8 am at 15 mph
    • Harry and Ron met each other at Q

To find:
    • The distance from Q, where Ron met Professor Snape

Approach and Working:
As Harry and Ron crossed checkpoint P at 9 am and 10 am, we can say
    • At 10 am, the distance between Harry and Ron = distance covered by Harry in 1 hour = 30 miles

Now, the speeds of Harry and Ron is 30 mph and 40 mph respectively, hence
    • From 10 am, Ron met Harry in \(\frac{30}{40 – 30}\) hours, or in 3 hours
      o Or, Ron met Harry at 1 pm at point Q

Professor Snape started cycling at the same direction as Harry and Ron, from point Q at 8 am, at a speed of 15 mph
Also, Harry and Ron reached point Q at 1 pm
    • At 1 pm, the distance already covered by Professor = \(15 * 5 = 75\) miles

Therefore, if Ron to meet Professor, then
    • Ron will take \(\frac{75}{40 – 15}\) hours = \(\frac{75}{25}\) hours = 3 hours from 1 pm
    • So, the distance Ron travelled from Q to the point where he met Professor
    = the distance travelled by Ron 3 hours = \(40 * 3 = 120\) miles

Hence, the correct answer is option D.

Answer: D

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Re: While driving on a highway, Harry and Ron crossed checkpoint P at 9 am  [#permalink]

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New post 10 Mar 2019, 20:03
EgmatQuantExpert wrote:
e-GMAT Question of the Week #4


While driving on a highway, Harry and Ron crossed checkpoint P at 9 am and 10 am, at individual speeds of 30 mph and 40 mph respectively. Professor Snape started cycling in the same direction as Harry and Ron, from point Q at 8 am at 15 mph. If Harry and Ron met each other at Q, then at what distance from Q Ron met Professor?

    A. 40
    B. 60
    C. 80
    D. 120
    E. 160


We see that Harry drove 1 hour more than Ron. If we let t = the number of hours Harry drove, then t - 1 = the number of hours Ron drove, and the distance between points P and Q can be determined by the following equation:

30t = 40(t - 1)

30t = 40t - 40

-10t = -40

t = 4

Therefore, the distance between P and Q is 30(4) = 120 miles. Since Professor Snape left Q at 8 am, he had biked 1 more hour than Harry (or 2 more hours than Ron). In the other words, he had biked 5 hours for 5 x 15 = 75 miles when Harry and Ron arrived at Q at the same time. Thus, Professor Snape had a 75-mile head start over Ron. If we let s = the number of hours it took Ron to catch up with the professor, starting from point Q, we can create the equation:

40s = 15s + 75

25s = 75

s = 3

Since it took Ron 3 hours to catch up with the professor starting from point Q, he had driven 40(3) = 120 miles from point Q.

Answer: D
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Re: While driving on a highway, Harry and Ron crossed checkpoint P at 9 am   [#permalink] 10 Mar 2019, 20:03
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