The cyclist rode from one point to another. He traveled the first third of the way at a speed of v1 = 18 km / h. Then, for half of the remaining time, he drove at a speed of v2 = 22 km / h, after which he walked to the final destination at a speed of v3 = 5 km / h. Determine the average speed of the cyclist.
Suppose that the entire path was l = 30 km (you can take any number)
The first 10 km (one third of the way according to the condition of the problem) the cyclist traveled in:
t1 = 10/18 = 0.5556 h;
For the remaining 20 km, the cyclist spent 2t2 hours (t2 hours driving and t2 hours walking). Knowing the total distance and speeds in individual sections, we will compose the equation:
t2 * 22 + t2 * 5 = 20;
27t2 = 20;
t2 = 20/27 = 0.7407 hours;
2t2 = 1.4814 hours;
Total travel time:
ttot = 1.4814 + 0.5556 = 2.037 h;
Knowing the total distance traveled and the total travel time, we find the average speed:
vcp = l / ttotal = 30 / 2.037 = 14.728 km / h.
Answer: vcp = 14.728 km / h.
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