Multiple choice

Peter and Paul start simultaneously on 2 different cars from Point A and travel towards Point B at speeds of 52 kmph and 39 kmph respectively on the same road. As soon as Peter reaches Point B, he returns back to Point A on the same road and meets Paul on the way. How far from Point B do the two friends meet, if the distance between the 2 points is 70 kms?

  1. 12

  2. 10

  3. 15

  4. 80

  5. 75
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Peter's speed is 52 kmph, Paul's is 39 kmph. Distance is 70 km. Time for Peter to reach B is 70/52 hours. In that time, Paul travels 39 * (70/52) = 52.5 km. The distance between them is 70 - 52.5 = 17.5 km. They close this gap at a relative speed of 52 + 39 = 91 kmph. Time to meet = 17.5 / 91 = 0.1923 hours. Distance from B = 0.1923 * 52 = 10 km.

AI explanation

Let the meeting point be x km from Point B, meaning Peter travels 70 + x km and Paul travels 70 - x km. Since they travel for the same amount of time until they meet, the equation is (70 + x) divided by 52 equals (70 - x) divided by 39. Cross-multiply to get 39(70 + x) = 52(70 - x), which simplifies to 2730 + 39x = 3640 - 52x. Combining like terms gives 91x = 910, so x equals 10 km.

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