Multiple choice

Towns X and Y are separated by a 90 km highway. Rahul departs from X towards Y, while Rohan starts from Y towards X, both setting off at the same time. They cross paths exactly 2 hours after their journey begins. After meeting, Rahul reaches Y, 180 minutes later than Rohan reaches X. Determine the speed of Rahul in km/hr.

  1. 15

  2. 18

  3. 20

  4. 22

  5. 24
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A Correct answer
Explanation

Let speeds be Vr and Ro. They meet in 2 hours, so 2(Vr + Ro) = 90, Vr + Ro = 45. After meeting, Rahul takes time t1 = (Distance_Y_to_X) / Vr = (Ro * 2) / Vr. Rohan takes t2 = (Distance_X_to_Y) / Ro = (Vr * 2) / Ro. Given t1 = t2 + 3, solve the system of equations to find Vr = 15.

AI explanation

Let their speeds be x and y kmph, so their combined speed gives the first equation 2 multiplied by the quantity x plus y equals 90, which simplifies to x plus y equals 45. The remaining distance for Rahul after they meet is 2y, and for Rohan it is 2x, and since Rahul takes 180 minutes or 3 hours longer, the equation is 2y divided by x minus 2x divided by y equals 3. Solving the system of equations by substituting y equals 45 minus x gives x equals 15 kmph.

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