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7 problems match “harmonic mean”. Clear

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1. Average speed for a round trip ●●○○○ 20 ptsA car travels from point A to point B at 30 km/h and returns from B to A at 50 km/h, covering the same distance each way. Find its average speed for the whole round trip, in km/h.
2. Average speed on a round trip ●●○○○ 20 ptsA man travels from point A to point B at a speed of 20 km/h and returns from point B to point A at a speed of 30 km/h. The distance from A to B equals the distance from B to A. Find his average speed over the whole trip, in km/h.
3. Arithmetic mean from geometric and harmonic means ●●○○○ 20 ptsFind the arithmetic mean of two positive numbers whose geometric mean is 4 and whose harmonic mean is $\frac{16}{5}$.
4. Harmonic mean from the other means ●●○○○ 20 ptsFind the harmonic mean of two positive numbers whose arithmetic mean is $\frac{15}{2}$ and whose geometric mean is $6$.
5. Two numbers from mean conditions ●●●○○ 50 ptsFind two numbers whose arithmetic mean exceeds their geometric mean by $\frac{1}{2}$ and whose harmonic mean is $\frac{25}{26}$ less than their arithmetic mean.
6. Two numbers from their means ●●●○○ 50 ptsTwo positive numbers have an arithmetic mean that exceeds their geometric mean by $2$, and their geometric mean exceeds their harmonic mean by $1.6$. Find the two numbers.
7. Two numbers from three means ●●●○○ 50 ptsFind two positive numbers whose arithmetic mean exceeds their geometric mean by $2$ and whose harmonic mean is $3.6$ less than their arithmetic mean. Give them in increasing order.