Question

Из пунктов А и В, расстояние между которыми 94 км, отправились одновременно навстречу друг другу пешеход и велосипедист. Скорость велосипедиста на 16 км/ч больше скорости пешехода. Найдите скорость каждого, если известно, что встретились они через 4 ч и пешеход сделал в пути получасовую остановку.

Answer 1

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Answer 2

Problem Analysis

We are given two points, A and B, which are 94 km apart. A pedestrian and a cyclist start simultaneously from these points and move towards each other. The cyclist's speed is 16 km/h faster than the pedestrian's speed. After 4 hours, they meet, and the pedestrian takes a 30-minute break during the journey. We need to find the speed of each person.

Solution

Let's assume the speed of the pedestrian is x km/h. Then the speed of the cyclist will be x + 16 km/h.

We can calculate the distance covered by each person using the formula: distance = speed × time.

The pedestrian travels for 4 hours and takes a 30-minute break, so the total time the pedestrian is moving is 4 hours - 0.5 hours = 3.5 hours.

The cyclist travels for 4 hours continuously.

The total distance covered by both the pedestrian and the cyclist is 94 km.

Using the above information, we can set up the following equation:

Distance covered by the pedestrian + Distance covered by the cyclist = Total distance

x × 3.5 + (x + 16) × 4 = 94

Now we can solve this equation to find the value of x.

Let's calculate it step by step.

Calculation

x × 3.5 + (x + 16) × 4 = 94

Simplifying the equation:

3.5x + 4x + 64 = 94

7.5x + 64 = 94

Subtracting 64 from both sides:

7.5x = 30

Dividing both sides by 7.5:

x = 4

So, the speed of the pedestrian is 4 km/h.

The speed of the cyclist is 4 + 16 = 20 km/h.

Answer

The speed of the pedestrian is 4 km/h, and the speed of the cyclist is 20 km/h.

Please let me know if I can help you with anything else.