Question

Велосипедист подолав відстань між двома містами за 2год, а пішохід - за 6 год. Знайти їхні швидкості пішохода на 8 км/ год менша, ніж швидкість велосипедиста

Answer 1

Problem Analysis

We are given that a cyclist covers a distance between two cities in 2 hours, while a pedestrian covers the same distance in 6 hours. The pedestrian's speed is 8 km/h less than the cyclist's speed. We need to find the speeds of the cyclist and the pedestrian.

Solution

Let's assume the speed of the cyclist is x km/h. According to the given information, the speed of the pedestrian is 8 km/h less than the cyclist's speed, so the speed of the pedestrian is (x - 8) km/h.

We can use the formula distance = speed × time to find the distances covered by the cyclist and the pedestrian.

The distance covered by the cyclist is given as the same distance covered by the pedestrian. Let's denote this distance as d km.

Using the formula, we can write the following equations:

Distance covered by the cyclist = speed of the cyclist × time taken by the cyclist

d = x × 2 ---(1)

Distance covered by the pedestrian = speed of the pedestrian × time taken by the pedestrian

d = (x - 8) × 6 ---(2)

Now, we can solve these equations to find the values of x and (x - 8).

Solving the Equations

Let's solve equations (1) and (2) to find the values of x and (x - 8).

From equation (1), we have:

d = 2x ---(3)

From equation (2), we have:

d = 6(x - 8) ---(4)

Since both equations (3) and (4) represent the same distance d, we can equate them:

2x = 6(x - 8)

Simplifying the equation:

2x = 6x - 48

48 = 6x - 2x

48 = 4x

Dividing both sides by 4:

12 = x

So, the speed of the cyclist is 12 km/h.

Substituting this value of x into equation (1), we can find the distance d:

d = 2(12)

d = 24 km

The speed of the pedestrian is 8 km/h less than the speed of the cyclist, so the speed of the pedestrian is:

12 - 8 = 4 km/h

Answer

Therefore, the speed of the cyclist is 12 km/h and the speed of the pedestrian is 4 km/h.