Question

Из деревни в город в 8 часов утра вышел мальчик, а в 10 утра в том же направлении вышел мужчина.Через какое время мужчина догонит мальчика, если его скорость 6 км\ч, а скорость мальчика состовляет 1\2 скорости мужчины?

Answer 1

6:2=3 км/ч - скорость мальчика
3*2ч=6 км прошел мальчик один
6-3=3 км/ч - скорость сближения
6:3=2ч

Answer 2

Problem Analysis

We are given that a boy leaves a village for a city at 8:00 AM, and a man leaves in the same direction at 10:00 AM. We need to determine how long it will take for the man to catch up to the boy, given that the man's speed is 6 km/h and the boy's speed is half the man's speed.

Solution

To solve this problem, we can use the formula: time = distance / speed.

Let's assume that the distance between the village and the city is D km.

The boy starts 2 hours earlier than the man, so he has a head start of 2 * boy's speed km.

The relative speed between the man and the boy is the difference between their speeds, which is man's speed - boy's speed.

The time it takes for the man to catch up to the boy is given by: time = (D - 2 * boy's speed) / relative speed.

Substituting the given values, we have: time = (D - 2 * (1/2) * man's speed) / (man's speed - (1/2) * man's speed).

Simplifying the equation, we get: time = (D - man's speed) / (1/2 * man's speed).

Now, we can substitute the given values into the equation and solve for time.

Calculation

Given: - The man's speed is 6 km/h. - The boy's speed is half the man's speed, which is (1/2) * 6 = 3 km/h.

Substituting these values into the equation, we have: time = (D - 6) / (1/2 * 6).

Simplifying further, we get: time = (D - 6) / 3.

Since we don't have the value of D, we cannot calculate the exact time it will take for the man to catch up to the boy without knowing the distance between the village and the city.

Answer

To determine the time it will take for the man to catch up to the boy, we need to know the distance between the village and the city (D). Without this information, we cannot provide an exact answer.