Question

Из одного пункта в противоположных направлениях вышли два пешехода. Скорость первого пешехода 5 км/ч, а скорость второго составляет 80% скорости первого. Через некоторое время расстояние между ними стало 18 9/10 км, при чем первый пешеход прошел 10 5/6 км. Какой пешеход вышел раньше и на сколько?

Answer 1

1). 0.8 · 5 = 4 (км/ч) - скорость второго пешехода.
2). 10 5/6 ÷ 5 = 2 1/6 (ч.) - время 1-ого.
3). 18 9/10 - 10 5/6 = 8 1/15 (км) - 2-ой пешеход.
4). 8 1/15 ÷ 4 = 6 1/20 (ч.) - время 2-ого.
5). 6 1/20 - 2 1/6 = (посчитаешь)
Ответ: ...

Answer 2

Problem Analysis

Two pedestrians start walking from the same point in opposite directions. The speed of the first pedestrian is 5 km/h, and the speed of the second pedestrian is 80% of the speed of the first pedestrian. After some time, the distance between them becomes 18 9/10 km, and the first pedestrian has walked 10 5/6 km. We need to determine which pedestrian started earlier and by how much.

Solution

Let's assume that the first pedestrian started walking at time t=0.

The distance covered by the first pedestrian can be calculated using the formula: distance = speed × time.

Let's denote the time taken by the first pedestrian as t1 and the time taken by the second pedestrian as t2.

The distance covered by the first pedestrian is given as 10 5/6 km, so we have: 10 5/6 = 5 × t1.

The distance covered by the second pedestrian is given by 18 9/10 km minus the distance covered by the first pedestrian: 18 9/10 - 10 5/6 = (80/100) × 5 × t2.

We can simplify the equations as follows: 10 5/6 = 5 × t1, 18 9/10 - 10 5/6 = (4/5) × 5 × t2.

Now, let's solve these equations to find the values of t1 and t2.

Calculation

To solve the equations, we need to convert the mixed fractions to improper fractions.

Converting 10 5/6 to an improper fraction: 10 5/6 = (10 × 6 + 5)/6 = 65/6.

Converting 18 9/10 to an improper fraction: 18 9/10 = (18 × 10 + 9)/10 = 189/10.

Substituting the values into the equations: 65/6 = 5 × t1, 189/10 - 65/6 = (4/5) × 5 × t2.

Simplifying the equations: t1 = (65/6) ÷ 5, t2 = (189/10 - 65/6) ÷ (4/5).

Now, let's calculate the values of t1 and t2.

Calculating t1: t1 = (65/6) ÷ 5 = (65/6) × (1/5) = 65/30 = 13/6.

Calculating t2: t2 = (189/10 - 65/6) ÷ (4/5) = [(189/10) × (5/4) - (65/6) × (5/4)] = (189/2 - 65/2) ÷ (4/5) = (124/2) ÷ (4/5) = (124/2) × (5/4) = 62 × (5/4) = 310/4 = 155/2.

Now, we have the values of t1 and t2. Let's compare them to determine which pedestrian started earlier.

Comparing t1 and t2: t1 = 13/6, t2 = 155/2.

Since t1 is smaller than t2, the first pedestrian started earlier.

To find out by how much earlier the first pedestrian started, we can subtract t2 from t1: t1 - t2 = (13/6) - (155/2) = (13/6) - (465/6) = -452/6 = -226/3.

The negative value indicates that the second pedestrian started 226/3 units of time later than the first pedestrian.

Answer

Therefore, the first pedestrian started earlier by 226/3 units of time.