Multiple choice

Two cities, X and Y, are 60 km apart and connected by a straight highway. Rahul starts traveling from X to Y, while Priya starts from Y to X. They begin at the same time and cross each other exactly 2 hours after starting. If Rahul reaches Y exactly 1 hour 40 minutes after Priya reaches X, what is Rahul's speed in km per hour?

  1. 10 km/hr

  2. 12 km/hr

  3. 14 km/hr

  4. 16 km/hr

  5. a
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let speeds be R and P. They meet in 2 hours, so 2(R+P) = 60, meaning R+P = 30. Rahul takes 60/R hours and Priya takes 60/P hours. Given 60/R = 60/P + 5/3, substituting P = 30-R leads to a quadratic equation. Solving for R gives 12 km/hr.

AI explanation

Let Rahul's speed be x km/hr and Priya's speed be y km/hr; since they meet after 2 hours, the sum of their speeds is 60/2 = 30 km/hr. The meeting point is 2x km from X and 2y km from Y; Rahul takes 2y/x hours to reach Y after the meeting, and Priya takes 2x/y hours to reach X. Since Rahul reaches 1 hour 40 minutes (which is 5/3 hours) after Priya, the equation is (2y/x) - (2x/y) = 5/3. Substituting y = 30 - x gives a quadratic equation, where solving for x yields the valid speed of 12 km/hr for Rahul.

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