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Pls explain

by [email protected] » Wed Dec 18, 2013 9:46 pm
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
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by vipulgoyal » Wed Dec 18, 2013 10:16 pm
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
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by theCodeToGMAT » Wed Dec 18, 2013 10:50 pm
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]
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by GMATGuruNY » Thu Dec 19, 2013 4:09 am
[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.
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by [email protected] » Thu Dec 19, 2013 6:09 am
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.
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by [email protected] » Thu Dec 19, 2013 6:15 am
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.
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by GMATGuruNY » Thu Dec 19, 2013 8:14 am
[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.
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I unlock the best way for YOU to solve problems.

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