Question

Из двух деревень, расстояние между которыми 27 км, одновременно навстречу друг другу вышли две группы туристов. Через 3 ч встретились. Какая была скорость первой группы, когда скорость второй группы 5 км/ч.

Answer 1

7 км- скорость 2 групы

Answer 2

Problem Analysis

We have two groups of tourists who start walking towards each other from two different villages. The distance between the villages is 27 km. After 3 hours, the two groups meet. We need to find the speed of the first group, given that the speed of the second group is 5 km/h.

Solution

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

Let's assume the speed of the first group is x km/h. Since the two groups are walking towards each other, their combined speed is the sum of their individual speeds. Therefore, the combined speed of the two groups is x + 5 km/h.

We know that the distance between the villages is 27 km and the time it takes for the two groups to meet is 3 hours. Using the formula, we can set up the following equation:

27 = (x + 5) × 3

Now, let's solve this equation to find the value of x.

Calculation

To solve the equation, we can start by distributing the 3 on the right side of the equation:

27 = 3x + 15

Next, we can isolate x by subtracting 15 from both sides of the equation:

27 - 15 = 3x

Simplifying further:

12 = 3x

Finally, we can solve for x by dividing both sides of the equation by 3:

x = 12 / 3

Therefore, the speed of the first group is 4 km/h.

Answer

The speed of the first group of tourists was 4 km/h when the speed of the second group was 5 km/h.

Verification

Let's verify the answer using the given information and the calculated values.

The distance between the villages is 27 km. The first group of tourists is walking at a speed of 4 km/h, and the second group is walking at a speed of 5 km/h. After 3 hours, the two groups meet.

The distance traveled by the first group in 3 hours is 4 km/h × 3 h = 12 km.

The distance traveled by the second group in 3 hours is 5 km/h × 3 h = 15 km.

The sum of the distances traveled by both groups is 12 km + 15 km = 27 km, which is equal to the distance between the villages.

Therefore, the answer is verified.

Conclusion

The speed of the first group of tourists was 4 km/h when the speed of the second group was 5 km/h.