Question

Из двух поселков, расстояние между которыми 50 км, выехали одновременно навстречу друг другу два велосипедиста. Скорость одного велосипедиста 11 км/ч, а второго 14 км/ч. Через сколько часов велосипедисты встретятся?

Answer 1

50:(11+14)=50:25=2 часа
Ответ: через 2 ч. велосипедисты встретятся

Answer 2

Problem Analysis

We have two cyclists traveling towards each other from two different villages. The distance between the villages is 50 km. The first cyclist has a speed of 11 km/h, and the second cyclist has a speed of 14 km/h. We need to determine how many hours it will take for the cyclists to meet.

Solution

To solve this problem, we can use the formula:

Time = Distance / Speed

Let's calculate the time it will take for the cyclists to meet.

Calculation

The total distance between the two villages is 50 km. Since the cyclists are traveling towards each other, the effective distance they need to cover is the sum of their individual distances.

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

The distance covered by the first cyclist is given by:

Distance1 = Speed1 * t1

The distance covered by the second cyclist is given by:

Distance2 = Speed2 * t2

Since the total distance covered by both cyclists is equal to the distance between the villages, we have:

Distance1 + Distance2 = 50 km

Substituting the expressions for Distance1 and Distance2, we get:

Speed1 * t1 + Speed2 * t2 = 50 km

We also know that the time taken by both cyclists is the same, so we have:

t1 = t2

Substituting this into the previous equation, we get:

Speed1 * t1 + Speed2 * t1 = 50 km

Simplifying the equation, we have:

(Speed1 + Speed2) * t1 = 50 km

Finally, we can solve for t1:

t1 = 50 km / (Speed1 + Speed2)

Let's substitute the given values and calculate the time it will take for the cyclists to meet.

Calculation

The speed of the first cyclist is 11 km/h, and the speed of the second cyclist is 14 km/h.

Substituting these values into the equation, we get:

t1 = 50 km / (11 km/h + 14 km/h)

Calculating the sum of the speeds, we have:

t1 = 50 km / 25 km/h

Simplifying the equation, we get:

t1 = 2 hours

Therefore, it will take the cyclists 2 hours to meet.

Answer

The cyclists will meet after 2 hours.