Multiple choice

A and B started simultaneously from M and N towards N and M, respectively. If the speed of A is 50% more than that of B, they can meet at 180 km from M. At what distance from N will they meet if the speed of A is twice that of B?

  1. 240 km

  2. 200 km

  3. 120 km

  4. 100 km

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let speed of B be v, A be 1.5v. They meet at 180 km from M. Distance MN = D. A travels 180, B travels D-180. Time is same: 180/(1.5v) = (D-180)/v. 120 = D-180 => D=300. Case 2: A speed 2v, B speed v. A travels x, B travels 300-x. x/(2v) = (300-x)/v. x = 600-2x => 3x=600 => x=200. Distance from N = 300-200 = 100 km.

AI explanation

When A is 50 percent faster, their speed ratio is 3 to 2, so the distance ratio is also 3 to 2, making the total distance 5 parts and each part equals 180 divided by 3, or 60 km, for a total of 300 km. When A is twice as fast, their new speed ratio is 2 to 1, making the meeting distance from N equal to 1 part of the total 3 parts. Therefore, the meeting distance from N is 300 divided by 3, which is 100 km.

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