Timework30

0. Two runners run in the same direction along a circular track 2 km long. The faster runner overtakes the slower one every 30 minutes. What are their speeds, if faster one completes a round one minute sooner than the other?

Answer
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Option : A
Explanation :
Let n₁ and n₂ be the speeds in km/hr and let n_j be the greater speed i.e., n₁ > n₂

⇒ n₁ - n₂ = 4
⇒ n₁ = 4 + n₂
⇒ n₂(4 + n₂)= 120 x 4
⇒ n₂² + 4n₂ - 480 = 0
⇒ n₂ = 20 or -24 (rejected)
∴ n₁ = 4 + n₂ = 24km/hr
Hence speeds are 24 km/hr and 20 km/hr
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