Multiple choice

In covering a distance of $30$ km, Abhay takes $2$ hours more than Sameer. If Abhay doubles his speed, then he would take $1$ hour less than Sameer. What is Abhay's speed? (in km/hr)

  1. $2$
  2. $3$
  3. $4$
  4. $5$
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D Correct answer
Explanation

Let Abhay's speed be v. 30/v - 30/(2v) = 2 - (-1) = 3. 30/v - 15/v = 3, so 15/v = 3, v = 5 km/hr.

AI explanation

Let Abhay's speed be x km/hr and Sameer's usual time be t hours. The first condition gives the equation 30/x = t + 2, and the second condition from doubling his speed gives 30/(2x) = t - 1. Subtracting the second equation from the first eliminates t, resulting in 30/x - 15/x = 3. Simplifying this yields 15/x = 3, which means x equals 5 km/hr.

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