Running around...and around...and around

Since they are running in opposite directions and meet every 15 seconds, they run a combined 1 lap every 15 seconds. In 15 seconds, Donovan runs $\frac{15}{40}$ of a lap, so Carl must run $1-\frac{15}{40} = \frac{25}{40}$ of a lap.

Thus, in 1 second, Carl runs $\frac{\frac{25}{40}}{15} = \frac{1}{24}$ of a lap, so it takes him 24 seconds to run 1 lap.

Donovan completes a lap in 40 sec. Lets assume length of lap is 40 units. So in 15 sec, Donovan completes 15 units and meets Carl for 1st time. That means Carl completed (40-15)=25 units in opposite direction in 15 sec. That is, 5units every 3 seconds.

Carl has to complete 15 more units - which he can do in 9 more seconds. So total time taken by Carl is 24 seconds.

Let speed of donovan be x and that of Carl be y so total distance is 40x now 15(x+y)=40x. So x/y=5/3 sox/y=time taken by x/time taken by y so y=40*3/5=24. So answer is 24 seconds

Suppose two person G and B are running on track.

G runs x(m/s) then track length = 40x(m). B runs y(m/s) ; covered length by B in 15s is = 15y(m).

Covered length by G in 15s is = 15x(m).

Rest length covered by B = 40x-15x = 25x ( which is = 15y ). if 25x = 15y then 40x = 24y (track length)

Hence; B complete 1 lap in 24 seconds with speed y(m/s).

Let Carl completes 1 lap in x minutes. In 15 minutes together they complete 1 lap. So 15/40 + 15/x = 1 , So x = 24 minutes

Let us assume that the track is 120m.

D started running and completed the track in 40s.

His speed is 120m/40s = 3m/s.

Distance covered by D in 15 secs= 15s×3m/s=45m.

Now C started from the other direction so he covered 120m-45m=75m (when he met D) in 15s.

Speed of C=75m/15s =5m/s.

Time taken to complete 120m = (120m)/(5m/s)=24s.

Let the Length of the Track be K meters.

Let time taken by Carl to Complete a Lap be M seconds.

Speed of Donovan = (K/40) m/s

Speed of Carl = (K/M) m/s

According to question, they meet every 15 seconds, Let X be the distance travelled by Carl from Lap Point to the Point where they both meet. Then,

X/(Speed of Carl) = (K-X)/(Speed of Donovan) = 15 Seconds....

Firstly, (K-X)/(K/40) = 15

or, 40(K-X)/K = 15

or, 40[1-(X/K)] = 15

or, (X/K)= 1 - (15/40) = (5/8)....(i)

Secondly, X/(K/M) = 15

or, M = 15(K/X) = 15(8/5) = 24...

or, M = 24 Seconds....Ans...

Let x be the total length of the path in meters, and t be the time in seconds required for Carl to take the lap. The speed of Donovan is $\frac {x}{40}$ , so in 15 seconds he travelled $\frac {x}{40} \times 15$ meters. Similarly Carl travelled $\frac {x}{t} \times 15$ meters. Let they start from the same point. They ran in opposite directions and they met after 15 seconds, so the sum of the distance they have travelled should equal the path length x. Thus we have $\frac {x}{40} \times 15 + \frac {x}{t} \times 15 = x$ . We can divide each side by x and we get t = 24 seconds

AFter 15 seconds, Donavan has run 15/40 of a lap and Carl 25/40 of a lap. 15/x = 25/40 -> x=24

They meet every 15 seconds. 1 second they run 1/15 of a lap.

Donovan run 1/40 of a lap, so Carl run 1/15 - 1/40 = 1/24 of a lap.

Therefore it takes Carl $\boxed{24}$ seconds to complete a lap.