Multiple choice

On a straight highway, points C and D are located such that point D is 360 km East of point C. Car P starts from point C, and car Q starts from point D at the same time. If they both move towards each other, they meet after 2 hours. If they both move in the same direction, they meet in 6 hours. What are their speeds?

  1. 120 kmph and 60 kmph

  2. 126 kmph and 54 kmph

  3. 130 kmph and 50 kmph

  4. 100 kmph and 50 kmph
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let speeds be u and v. When moving towards each other, relative speed is u + v = 360/2 = 180. When moving in the same direction, relative speed is |u - v| = 360/6 = 60. Solving u + v = 180 and u - v = 60 gives u = 120 and v = 60.

AI explanation

Using the relative speed concept for two bodies moving towards each other, the sum of their speeds (v1 plus v2) equals 360 divided by 2, which is 180 kmph. When moving in the same direction, their relative speed (v1 minus v2) equals 360 divided by 6, which is 60 kmph. Adding these two equations gives 2 times v1 equals 240, so v1 is 120 kmph. Subtracting the second equation from the first gives 2 times v2 equals 120, meaning v2 is 60 kmph. The speeds are 120 kmph and 60 kmph.

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