Anand starts from a point P towards point Q, where PQ = 90 : GMAT Problem Solving (PS)
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# Anand starts from a point P towards point Q, where PQ = 90

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Anand starts from a point P towards point Q, where PQ = 90 [#permalink]

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03 Sep 2011, 07:22
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Anand starts from a point P towards point Q, where PQ = 90 km. After 1 hour, Ram starts from P and catches up with Anand after 2 more hours. After meeting they continue to travel towards Q. On reaching Q, Ram reverses his direction and meets Anand 6 hours after the first meeting. Find Anand's speed.

(A) (45/7) kmph
(B) (60/7) kmph
(C) (40/7) kmph
(D) (30/7) kmph
(E) (65/7) kmph
[Reveal] Spoiler: OA

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petrifiedbutstanding

Last edited by Bunuel on 13 Jul 2013, 06:19, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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03 Sep 2011, 07:58
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petrifiedbutstanding wrote:
Found this exercise in a random book.

Anand starts from a point P towards point Q, where PQ = 90 km. After 1 hour, Ram starts from P and catches up with Anand after 2 more hours. After meeting they continue to travel towards Q. On reaching Q, Ram reverses his direction and meets Anand 6 hours after the first meeting. Find Anand's speed.

(A). (45/7) kmph
(B). (60/7) kmph
(C). (40/7) kmph
(D). (30/7) kmph
(E). (65/7) kmph

Can someone help with this, please?

Let the first meeting point be at a distance of x km from P, the remaining distance until Q would be (90-x) km

Anand traveled this x kms in 3 hours, making his speed x/3 kmph
Ram traveled the same x kms in 2 hours, making his speed x/2 kmph

So, in 6 hours:
Anand will cover=6x/3=2x km
Ram will cover=6x/2=3x km

And between their first meeting point and second, they both together covered a distance of 2(90-x) km.

2x+3x=2(90-x)
5x=180-2x
7x=180
x=180/7 km

Anand's speed=x/3=180/(3*7)=60/7 kmph

Ans: "B"
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04 Sep 2011, 09:00
fluke wrote:
petrifiedbutstanding wrote:
Found this exercise in a random book.

Anand starts from a point P towards point Q, where PQ = 90 km. After 1 hour, Ram starts from P and catches up with Anand after 2 more hours. After meeting they continue to travel towards Q. On reaching Q, Ram reverses his direction and meets Anand 6 hours after the first meeting. Find Anand's speed.

(A). (45/7) kmph
(B). (60/7) kmph
(C). (40/7) kmph
(D). (30/7) kmph
(E). (65/7) kmph

Can someone help with this, please?

Let the first meeting point be at a distance of x km from P, the remaining distance until Q would be (90-x) km

Anand traveled this x kms in 3 hours, making his speed x/3 kmph
Ram traveled the same x kms in 2 hours, making his speed x/2 kmph

So, in 6 hours:
Anand will cover=6x/3=2x km
Ram will cover=6x/2=3x km

And between their first meeting point and second, they both together covered a distance of 2(90-x) km.

2x+3x=2(90-x)
5x=180-2x
7x=180
x=180/7 km

Anand's speed=x/3=180/(3*7)=60/7 kmph

Ans: "B"

Nice solution. I made it much more complicated...

I used - 3A=2R
8R=90+x
9A=90-x

solving giving the same result - but i guess it took me longer than to you and increased my chances to make mistakes...
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04 Sep 2011, 09:08
yup nice and easy one fluke!! kudos for the wonderfully solving the problem in 3 steps
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04 Sep 2011, 09:30
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Speed of Anand =a
'" Ram=r
Till Anand and Ram meets, Anand travels for 3 hrs, and Ram trvels for 2 HRs
When Two people meet, the distance travelled by them is equal
=>> 3a = 2r
which gives r = 3a/2------------(i)
Now for next 6 hrs, Anand travels 6a Kms and Ram trvls 6r Kms.

Refer the pic:
....(3a)......||...........(6a)..................|||...............
P|_________||______________________|||_________Q
....(2r)......||..............................(6r)....................

The (6r) covers the distance from (|| to Q)plus( Q to ||| )
PQ = 90
2PQ = 180
3a + 6a + 6r + 2r = 180
9a + 8r = 180
9a + 8*3a/2 = 180 -----using (i)
9a + 12a = 180
a = 180/21 = 60/7

From this
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04 Sep 2011, 10:41
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Let a be Anand's speed and r be Ram's speed.When Ram and Anand meet for the first time, distance travelled by them is the same
=> a(3) = r(2)
When Ram and Anand meet for the second time, they have travelled twice the distance PQ, or 180 km, together
=> a(9) + r(8) = 180

Solving these equations for a, we get a = 180/21 = 60/7 km/hr
=>Option (B)
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07 Sep 2011, 02:01
Thank you, fluke and GynaOne. Really simple solutions!
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07 Sep 2011, 06:23
Couldn get it the first time
Took more than 5 min to solve.
After looking at the solution it looked easy but I was stumped
Have a small doubt.. On GMAT wats the probability of facing these kind of questions ??
And at what level??

-cheers
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Re: Anand starts from a point P towards point Q, where PQ = 90 [#permalink]

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03 Oct 2013, 09:40
why the distance covered is 2(90-x) ? ram meets anand after 6hrs on first meet.
so not necessary that anand would have travelled same distance as ram did.?

bunuel help ?
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Re: Anand starts from a point P towards point Q, where PQ = 90 [#permalink]

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03 Oct 2013, 13:26
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I solved it like this:

Let R = Ram's speed
A = Anand's speed

Since it took Ram 2 hours to cover the same distance as Anand did in 3 hours we know

2R = 3A
R = (3/2)A

We know they don't meet again for another 6 hours, at which point Anand will have been traveling for 9 hours to a distance I'll call "D". Ram will have been traveling for only 8 hours when he reaches D and the total distance he will have traveled is 90 + (90 - D) = 180 - D

So:

9A = D
8R = 180 - D or 180 - 8R = D

180 - 8R = 9A

Substitute for R

180 - 8(3/2)A = 9A
180 - 12A = 9A
180 = 21A
60/7 = A
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Re: Anand starts from a point P towards point Q, where PQ = 90 [#permalink]

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06 Oct 2013, 05:19
sunny3011 wrote:
why the distance covered is 2(90-x) ? ram meets anand after 6hrs on first meet.
so not necessary that anand would have travelled same distance as ram did.?

bunuel help ?

Same question: Why is it 2(90-x)? I understand why we need the first (90-x), but why is it assumed that they meet at the same point X when they're headed back?
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Re: Anand starts from a point P towards point Q, where PQ = 90 [#permalink]

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17 Oct 2013, 03:39
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pauc wrote:
sunny3011 wrote:
Anand starts from a point P towards point Q, where PQ = 90 km. After 1 hour, Ram starts from P and catches up with Anand after 2 more hours. After meeting they continue to travel towards Q. On reaching Q, Ram reverses his direction and meets Anand 6 hours after the first meeting. Find Anand's speed.

(A) (45/7) kmph
(B) (60/7) kmph
(C) (40/7) kmph
(D) (30/7) kmph
(E) (65/7) kmph

why the distance covered is 2(90-x) ? ram meets anand after 6hrs on first meet.
so not necessary that anand would have travelled same distance as ram did.?

bunuel help ?

Same question: Why is it 2(90-x)? I understand why we need the first (90-x), but why is it assumed that they meet at the same point X when they're headed back?

Look at the diagram below:
Attachment:

Untitled4.png [ 2.58 KiB | Viewed 2127 times ]
Blue dot is the second meeting point.

In blue is the distance covered by Anand after the first meeting.
In green is the distance covered by Ram after the first meeting.

Their sum is twice 90-x.

Hope it's clear.
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Re: Anand starts from a point P towards point Q, where PQ = 90 [#permalink]

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17 Oct 2013, 08:00
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Here is a quick approach- since we know the time taken by anand : time taken by ram (same distance when they meet after 3 hrs) = 3 : 2. therefore, ratio of their speed= 2 : 3.
Let speed be 2x, 3x.
Now in three hours distance covered = 6x. remaining 90-6x covered twice in 6 hours.
=> 12x + 18x = 2(90-6x) giving 2x (remember this is the speed of anand and not just x) = 60/7
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Re: Anand starts from a point P towards point Q, where PQ = 90 [#permalink]

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17 Oct 2013, 08:56
I don't get this problem at all; you don't know how long it takes Ram to reach the end point and then turn back, so you can't calculate anything for certain...there's too many variables here.
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Re: Anand starts from a point P towards point Q, where PQ = 90 [#permalink]

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17 Oct 2013, 08:58
AccipiterQ wrote:
I don't get this problem at all; you don't know how long it takes Ram to reach the end point and then turn back, so you can't calculate anything for certain...there's too many variables here.

Check solutions above. You can use only one variable to solve.
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Anand starts from a point P towards point Q, where PQ = 90 [#permalink]

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24 Jun 2014, 21:05
Since Anand takes 3 hrs to travel the distance that Ram travels in 2 hrs their speed is in the ratio 2:3. We also know s1=(90-x)/9 and s2=(90+x)/8 where s1 and s2 are the speed of Anand and Ram resp.
(90-x) /9 / (90+x)/8 = 2/3
From the above equations we get s1=60/7
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Re: Anand starts from a point P towards point Q, where PQ = 90 [#permalink]

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Re: Anand starts from a point P towards point Q, where PQ = 90 [#permalink]

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