Discussion

Explanation:

Let S be the starting point of the race, and A and B run at speeds of S_A and S_B, respectively.

a is the point where A and B meet for the first time and b is the point where A and B meet for the second time.

When they meet, A and B have covered different distances in the same time. 

So, the ratio of the distances covered by them is the same as the ratio of their speeds. 

When they meet for the first time, distance travelled by A = 900 and let X be the distance travelled by B.

So, $\frac{S_A}{S_B}=\frac{900}{X}$ …(i)

Now when they meet for the second time, distance travelled by A is X - 600 and distance travelled by A = 900 + 600.

So, $\frac{S_A}{S_B}=\frac{X-600}{900+600}=\frac{X-600}{1500}$ …(ii)

∴ from the 2 equations

900/X = (X - 600)/1500

⇒ X² – 600X – 1500 × 900 = 0

⇒ X = 1500

∴ Length of the track = 900 + 1500 = 2400 m

Hence, option (a).

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