Question

7. Розв'яжи задачу. З двох оздоровчих таборів, відстань між якими 700 м, одночасно вийшли дві групи дітей і пішли в протилежних напрямках, одна з груп зі швидкістю 72 м/хв. Через 35 хв відстань між групами стала 5 км 670 м. З якою швидкістю рухалася друга група, якщо обидві рухались рівномірно?​

Answer 1

                            А --------------- 700 м --------------- В

      72 м/мин <-----                 t = 35 мин                -----> ? м/мин

1) 5 670 - 700 = 4 970 (м) - пройдут обе группы за 35 мин;

2) 72 · 35 = 2520 (м) - пройдёт одна группа;

3) 4 970 - 2 520 = 2 450 (м) - пройдёт другая группа;

4) 2 450 : 35 = 70 (м/мин) - скорость другой группы.

Ответ: 70 м/мин - рухалася друга група.

Answer 2

Problem Analysis

We are given that two groups of children left two health camps simultaneously and walked in opposite directions. The distance between the camps is 700 m. One group walked with a speed of 72 m/min. After 35 minutes, the distance between the groups became 5 km 670 m. We need to find the speed of the second group if both groups were moving at a constant speed.

Solution

Let's assume the speed of the second group is x m/min.

After 35 minutes, the first group has covered a distance of 72 m/min * 35 min = 2520 m.

The distance between the two groups is now 5 km 670 m, which is equal to 5670 m.

Since the groups are moving in opposite directions, the total distance covered by both groups is the sum of the distances covered by each group.

So, the total distance covered by both groups is 2520 m + 5670 m = 8190 m.

Since the total distance covered is equal to the sum of the distances covered by each group, we can write the equation:

2520 m + x m/min * 35 min = 8190 m

Simplifying the equation:

2520 m + 35x m = 8190 m

35x m = 8190 m - 2520 m

35x m = 5670 m

Dividing both sides of the equation by 35 m:

x = 5670 m / 35 m

x = 162 m/min

Therefore, the second group was moving at a speed of 162 m/min.