$$AB$$ is a straight road of length 400 metres. From $$A$$, Samrud runs at a speed of $$6 \text{ m/s}$$ towards $$B$$ and at the same time Saket starts from $$B$$ and runs towards $$A$$ at a speed of $$5 \text{ m/s}$$. After reaching their destinations, they return with the same speeds. They repeat it again and again. How many times do they meet each other in 15 minutes?
Solution
In 15 minutes, that is 900 seconds, the two runners together cover $$(6 + 5) \times 900 = 9900$$ metres. Along a road of length 400 metres they come together once for every 400 metres of combined running. Since $$\frac{9900}{400} = 24.75$$, exactly 24 such meetings are completed, so they meet 24 times.
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