Joy and Kat run around a circular track of length 1100 m in opposite directions with initial speed of 6 m/sec and 4 m/sec, respectively. Starting from the same point whenever they meet, Joy's speed halves and Kat's speed doubles. After how much time from the beginning will they meet for the second time?

Step 1: First Meeting
Total distance to cover for the first meeting = length of the track = 1100 m

Initial speed of Joy (S
J
​
) = 6 m/sec

Initial speed of Kat (S
K
​
) = 4 m/sec

Since they run in opposite directions, their relative speed is:

Relative Speed
1
​
=S
J
​
+S
K
​
=6+4=10 m/sec
Time taken for the first meeting (T
1
​
):

T
1
​
=
Relative Speed
1
​

Distance
​
=
10
1100
​
=110 sec
Step 2: Second Meeting

Immediately after the first meeting, Joy's speed halves:

New S
J
​
=
2
6
​
=3 m/sec
Kat's speed doubles:

New S
K
​
=4×2=8 m/sec
Their new relative speed in opposite directions is:

Relative Speed
2
​
=3+8=11 m/sec
Time taken from the first meeting to the second meeting (T
2
​
):

T
2
​
=
Relative Speed
2
​

Distance
​
=
11
1100
​
=100 sec
Step 3: Total Time
Total time from the beginning until the second meeting:

Total Time=T
1
​
+T
2
​
=110+100=210 sec