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Half the distance at one speed, the rest in two equal time intervals at two other speeds: average speed

The same question, asked 2 times: 30 Jan 2023*, 9 Apr 2024. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    30 Jan 2023

    23
    A horse rider covers half the distance with 5 m/s5\text{ }m/s speed. The remaining part of the distance was travelled with speed 10 m/s10\text{ }m/s for half the time and with speed 15 m/s15\text{ }m/s for other half of the time. The mean speed of the rider averaged over the whole time of motion is x7 m/s\frac{x}{7}\text{ }m/s. The value of xx is

  2. Question 2

    9 Apr 2024

    2
    A particle moving in a straight line covers half the distance with speed 6 m/s6\text{ }m/s. The other half is covered in two equal time intervals with speeds 9 m/sm/s and 15 m/s15\text{ }m/s respectively. The average speed of the particle during the motion is:

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