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One hour before John started walking from P to Q, a distance

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One hour before John started walking from P to Q, a distance  [#permalink]

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New post 15 Apr 2014, 15:28
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Question Stats:

66% (01:35) correct 34% (01:54) wrong based on 118 sessions

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One hour before John started walking from P to Q, a distance of 18 miles, Ann had started walking along the same road from Q to P. Ann walked at a constant speed of 3 miles per hour and John at 2 miles per hour. How many miles had Ann walked when they met?

A. 6 miles
B. 8,4 miles
C. 9 miles
D. 9,6 miles
E. 12 miles
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Re: One hour before John started walking from P to Q  [#permalink]

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New post 15 Apr 2014, 19:00
In an hour Ann walked 3 miles. So when John started to walk the distance between the two was 15 miles. Add their respective rates together (3mph + 2mph = 5mph) and calculate how long it took them to cover the 15 miles at that combined rate (15miles/5mph = 3hrs)

So in 3 hours Ann walks 3mph*3hrs = 9miles. Last step is to add in the initial 3 miles she walked before John started.

9+3=12miles
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Re: One hour before John started walking from P to Q  [#permalink]

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New post 15 Apr 2014, 20:53
tauchmeister wrote:
I'm having problems with the following question to,

It is from and old set I have with me,

I have no idea from the source.

One hour before John started walking from P to
Q, a distance of 18 miles, Ann had started walking
along the same road from Q to P. Ann walked at a
constant speed of 3 miles per hour and John at 2
miles per hour. How many miles had Ann walked
when they met?
a) 6 miles
b) 8,4 miles
c) 9 miles
d) 9,6 miles
e) 12 miles

Official answer E

Thanks


This is again a relative speed question and I would suggest you to check out the links given in my previous post.


Ann walks from Q to P at a speed of 3 miles/hr for one hour. She covers 3 miles in 1 hour and now distance between John and Ann is 18 - 3 = 15 miles.

Ann walks at 3 mph and John at 2 mph so their relative speed is 3+2 = 5 mph.

They have to cover 15 miles so it will take them 15/5 = 3 hours to meet.
In 3 hrs, Ann would have covered 3 hrs * 3 miles per hour = 9 miles.

Adding this to the 3 miles she covered before John, Ann covered a total of 3 + 9 = 12 miles.

Answer (E)

Another Method:
You can also use ratios to say that Ann and John have 15 miles between them (after Ann covers 3 miles) and their speeds are in the ratio 3:2. So Ann will cover 3/5 of the distance i.e. (3/5)*15 = 9 miles.
This gives a total distance of 3 + 9 = 12 miles
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Re: One hour before John started walking from P to Q  [#permalink]

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New post 15 Apr 2014, 21:41
Ann has already walked 3 Miles, so 15 Miles are remaining

Setting up the equation

\(\frac{15-x}{2} = \frac{x}{3}\)

x = 9

Distance covered by Ann = 9+3

Answer = 12 = E
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Re: One hour before John started walking from P to Q, a distance  [#permalink]

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New post 10 Sep 2015, 15:12
i am sorry for the silly question but how they meet and Ann moved before john and his speed is faster as well and eventually they meet. I think they never or I am missing something ?
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Re: One hour before John started walking from P to Q, a distance  [#permalink]

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New post 10 Sep 2015, 18:56
IN question itself some discrepancy,
it mentions onehour before john started .
then anna covered 9.6miles.

If question mentions anna started 1hour before then
anna covered 12 miles.

so in this context option D is correct.
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Re: One hour before John started walking from P to Q, a distance  [#permalink]

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New post 10 Sep 2015, 20:44
hatemnag wrote:
i am sorry for the silly question but how they meet and Ann moved before john and his speed is faster as well and eventually they meet. I think they never or I am missing something ?


John walks from P to Q but Ann walks from Q to P. They are both walking toward each other so they meet.


Quote:
IN question itself some discrepancy,
it mentions onehour before john started .
then anna covered 9.6miles.

If question mentions anna started 1hour before then
anna covered 12 miles.

so in this context option D is correct.


The statement:

"One hour before John started walking from P to Q, a distance of 18 miles, Ann had started walking along the same road from Q to P"

One hour before John started ... Ann had started ...

So Ann had started one hour before John started. Not the other way around.
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Re: One hour before John started walking from P to Q, a distance  [#permalink]

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New post 25 Jul 2017, 11:50
tauchmeister wrote:
One hour before John started walking from P to Q, a distance of 18 miles, Ann had started walking along the same road from Q to P. Ann walked at a constant speed of 3 miles per hour and John at 2 miles per hour. How many miles had Ann walked when they met?

A. 6 miles
B. 8,4 miles
C. 9 miles
D. 9,6 miles
E. 12 miles


We have a converging problem in which we use the formula distance of John + distance of Ann = total distance.

We can let John’s time = t and Ann’s time = (t + 1). Furthermore, John’s distance is 2t and Ann’s distance is 3(t + 1) = 3t + 3. So, we have:

2t + 3t + 3 = 18

5t = 15

t = 3

Thus, Ann traveled 3t + 3 = (3 x 3) + 3 = 12 miles.

Answer: E
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Re: One hour before John started walking from P to Q, a distance  [#permalink]

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Re: One hour before John started walking from P to Q, a distance   [#permalink] 08 Apr 2019, 08:32
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