Two joggers are running around an oval track in opposite directions. One jogger runs around the track in 56 seconds. They meet every 24 seconds. How many seconds does it take the second jogger to run around the track?

To solve this problem, we can use the concept of relative speed. Let's assume that the second jogger takes 'x' seconds to run around the track.

The first jogger completes one lap in 56 seconds. Therefore, in 24 seconds, the first jogger would have completed 24/56 of a lap.

Since they meet every 24 seconds, the distance covered by both joggers combined is equal to one complete lap.

Hence, the distance covered by the first jogger in 24 seconds plus the distance covered by the second jogger in 24 seconds is equal to one lap:

(24/56) + (24/x) = 1

To simplify this equation, we can multiply through by the least common multiple of 56 and x, which is 56x:

24x + 24(56) = 56x

Now let's solve for 'x':

1344 = 32x

Divide both sides by 32:

x = 1344/32

Simplifying further, we find:

x = 42

Therefore, it takes the second jogger 42 seconds to run around the track.