From points A and B, the distance between which is equal to 27 km, two pedestrians simultaneously came out towards each other and met in 3 hours. The pedestrian who left A arrives at B 1 hour 21 minutes earlier than the second arrives at A. Find the speed of each pedestrian.
Solution: To solve this problem, we introduce two conditional variables “X” and “Y”, through which we denote the speed of movement of pedestrians leaving points A and B, respectively. Then, according to the problem statement, we compose the following equations: 1) 27 / (X + Y) = 3; 2) 27 / X + 1.35 = 27 / Y. Solving a system of two equations with two unknowns, we get the quadratic equation 1.35X ^ 2 + 41.85X – 243 = 0. Solving this quadratic equation, we get two roots X1 = 5 kilometers per hour and X2 = -36 kilometers per hour. Since the speed is positive, the correct answer is 5 km / h. Therefore, the speed of the second pedestrian is 9 – 5 = 4 kilometers per hour.
Answer: 5 km / h and 4 km / h.
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