Question

Турист прошел 6 км от станции до поселка и вернулся обратно на велосипеде,затратив на весь путь 2 часа.на велосипеде он ехал со скоростью на 8 км/ч большей,чем шел пешком.с какой скоростью турист шел пешком ?

Answer 1

Уравнение составлял! !!

Answer 2

Problem Analysis

A tourist walked 6 km from a station to a village and then returned back on a bicycle, taking a total of 2 hours for the entire journey. The tourist cycled at a speed that was 8 km/h faster than their walking speed. We need to determine the speed at which the tourist was walking.

Solution

Let's assume the speed at which the tourist was walking is x km/h.

We know that the distance covered while walking is 6 km, and the distance covered while cycling is also 6 km.

The time taken to walk 6 km at a speed of x km/h can be calculated using the formula: time = distance / speed.

Similarly, the time taken to cycle 6 km at a speed of (x + 8) km/h can be calculated using the same formula.

Since the total time taken for the entire journey is 2 hours, we can set up the following equation:

(6 / x) + (6 / (x + 8)) = 2

Let's solve this equation to find the value of x.

Calculation

To solve the equation (6 / x) + (6 / (x + 8)) = 2, we can multiply both sides of the equation by x(x + 8) to eliminate the denominators:

x(x + 8) * (6 / x) + x(x + 8) * (6 / (x + 8)) = 2 * x(x + 8)

Simplifying the equation:

6(x + 8) + 6x = 2x(x + 8)

Expanding and simplifying further:

6x + 48 + 6x = 2x^2 + 16x

Combining like terms:

12x + 48 = 2x^2 + 16x

Rearranging the equation to form a quadratic equation:

2x^2 + 4x - 48 = 0

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

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a), where a = 2, b = 4, and c = -48.

Calculating the discriminant: b^2 - 4ac = 4^2 - 4 * 2 * -48 = 16 + 384 = 400

Taking the square root of the discriminant: √400 = 20

Using the quadratic formula to find the values of x:

x = (-4 + 20) / (2 * 2) = 16 / 4 = 4

x = (-4 - 20) / (2 * 2) = -24 / 4 = -6

Since the speed cannot be negative, we discard the negative value of x.

Answer

Therefore, the tourist was walking at a speed of 4 km/h.

Verification

Let's verify the answer by substituting the value of x into the equation:

(6 / 4) + (6 / (4 + 8)) = 2

Simplifying the equation:

1.5 + 0.5 = 2

The equation is true, which confirms that the tourist was walking at a speed of 4 km/h.