let a(anand) and r(Ram) meet at point x between PQ ,remaining distance = 90 - x
a travels this distance in 3 hours and r travles this in 2 hours
hence a speed = x/3 and r speed = x/2
It took 6 hours to meet next time let that the point be y
P--------------||x -----------||Y-----Q
---------------||X----------A>|| y<--R--Q
a was moving towards y and r was returning from q towards y
so in six hours distance travelled by a and r = 2x+3x = 2(90-x)
x=180/7 km
Anand's speed=x/3=180/(3*7)=60/7 kmph

Let speed of Anand be "A" and Ram be "R"

Distance travelled by Anand in 1 Hr = A*1 = A
Time to catch = GAP/(differenc of speed)
2 = GAP/(R-A)
2 = A/R-A ==> 2R - 2A = A ==> 2R = 3A

Total Distance travelled by Ram in 2+6 hours = 90+x ==> 90 + x = 8R
Total Distance travelled by Anand in 1+2+6 hours = 90-x ==> (90-x) = 9A

Dividing both
(90+x)/(90-x) = 8/9 * 3/2
(90+x)/(90-x) = 4/3
270 + 3x = 360 - 4x
x = 90/7

Speed of A = (90 - 90/7)/9 = 10 - 10/7 = 60/7

[spoiler]{B}[/spoiler]

[email protected] 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

Let a = Arnand's rate. and r = Ram's rate.

1st meeting:
Time for Arnand = 3 hours. (1 hour alone + 2 hours for Ram to catch up.)
Time for Ram = 2 hours.
Since the time ratio for Arnand and Ram = 3:2, their rate ratio is the RECIPROCAL:
a/r = 2/3
r = (3/2)a.

2nd meeting:
Ram travels the ENTIRE 90km and then backtracks to meet Arnand:
R---------90--------->
A-----------><------R
As the figure above shows, the total distance traveled by Ram and Arnand together = 180km.

The 2nd meeting takes places 6 hours after the 1st meeting.
Since Ram's time for the 1st meeting = 2 hours, his total time for the 2nd meeting = 2+6 = 8 hours.
Since Arnand's time for the 1st meeting = 3 hours, his total time for the 2nd meeting = 3+6 = 9 hours.

Distance traveled by Ram = r*t = (3/2)a * 8 = 12a.
Distance traveled by Arnand = a * 9 = 9a.
Since the total distance traveled is 180km, we get:
12a + 9a = 180
21a = 180
a = 180/21 = 60/7.

The correct answer is B.

Hey Mitch,


Im not clear as to how you got 180 KMs as the total distance!

Before Ram backtracks and meets Anand both of them are moving towards point q so when Ram backtracks what is Anand doing?

GMATGuruNY wrote:

[email protected] 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

Let a = Arnand's rate. and r = Ram's rate.

1st meeting:
Time for Arnand = 3 hours. (1 hour alone + 2 hours for Ram to catch up.)
Time for Ram = 2 hours.
Since the time ratio for Arnand and Ram = 3:2, their rate ratio is the RECIPROCAL:
a/r = 2/3
r = (3/2)a.

2nd meeting:
Ram travels the ENTIRE 90km and then backtracks to meet Arnand:
R---------90--------->
A-----------><------R
As the figure above shows, the total distance traveled by Ram and Arnand together = 180km.

The 2nd meeting takes places 6 hours after the 1st meeting.
Since Ram's time for the 1st meeting = 2 hours, his total time for the 2nd meeting = 2+6 = 8 hours.
Since Arnand's time for the 1st meeting = 3 hours, his total time for the 2nd meeting = 3+6 = 9 hours.

Distance traveled by Ram = r*t = (3/2)a * 8 = 12a.
Distance traveled by Arnand = a * 9 = 9a.
Since the total distance traveled is 180km, we get:
12a + 9a = 180
21a = 180
a = 180/21 = 60/7.

The correct answer is B.

Hey Mitch,


Im not clear as to how you got 180 KMs as the total distance!

Before Ram backtracks and meets Anand both of them are moving towards point q so when Ram backtracks what is Anand doing?

GMATGuruNY wrote:

[email protected] 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

Let a = Arnand's rate. and r = Ram's rate.

1st meeting:
Time for Arnand = 3 hours. (1 hour alone + 2 hours for Ram to catch up.)
Time for Ram = 2 hours.
Since the time ratio for Arnand and Ram = 3:2, their rate ratio is the RECIPROCAL:
a/r = 2/3
r = (3/2)a.

2nd meeting:
Ram travels the ENTIRE 90km and then backtracks to meet Arnand:
R---------90--------->
A-----------><------R
As the figure above shows, the total distance traveled by Ram and Arnand together = 180km.

The 2nd meeting takes places 6 hours after the 1st meeting.
Since Ram's time for the 1st meeting = 2 hours, his total time for the 2nd meeting = 2+6 = 8 hours.
Since Arnand's time for the 1st meeting = 3 hours, his total time for the 2nd meeting = 3+6 = 9 hours.

Distance traveled by Ram = r*t = (3/2)a * 8 = 12a.
Distance traveled by Arnand = a * 9 = 9a.
Since the total distance traveled is 180km, we get:
12a + 9a = 180
21a = 180
a = 180/21 = 60/7.

The correct answer is B.

[email protected] wrote:Hey Mitch,


Im not clear as to how you got 180 KMs as the total distance!

Before Ram backtracks and meets Anand both of them are moving towards point q so when Ram backtracks what is Anand doing?

Let A = the 1st meeting place and B = the 2nd meeting place.

For illustrative purposes:
Let A be 30km from P.
Let B be 60km from P (and thus 30km from Q).
The route looks like this:
P<---30km--->A<---30km--->B<---30km--->Q

To get to B:
Arnand travels 30km to A and then another 30km to B, for a total of 60km.
Ram travels 30km to A, then 60km to Q, then backtracks 30km to B, for a total of 120km.
Thus, to meet at B, the TOTAL distance that must be traveled by Arnand and Ram = 60+120 = 180km.