Question

От пристани вниз по реке отправили плот, что движется со скоростью 4км/час. Через 9 часов вслед за ним вышла лодка скорость которой 9 км,/час. На каком расстоянии лодка догонит плот?

Answer 1

За 9 часов плот прошел 36 километров
А далее -
Плот - 36+4+4+4+4+4
Лодка 9+9+9+9+9+9
За 6 часов догонит.

Answer 2

Problem Analysis

We are given that a raft is moving downstream with a speed of 4 km/h, and after 9 hours, a boat with a speed of 9 km/h starts following the raft. We need to determine the distance at which the boat catches up to the raft.

Solution

To solve this problem, we can use the concept of relative speed. The relative speed between the boat and the raft is the difference in their speeds.

Let's assume that the distance at which the boat catches up to the raft is D km.

Since the raft has been moving for 9 hours at a speed of 4 km/h, the distance covered by the raft in 9 hours is 9 * 4 = 36 km.

Now, let's consider the time taken by the boat to catch up to the raft. Since the boat is moving at a speed of 9 km/h and the raft is moving at a speed of 4 km/h, the relative speed between the boat and the raft is 9 - 4 = 5 km/h.

The time taken by the boat to catch up to the raft is given by the formula: Time = Distance / Speed

Substituting the values, we have: Time = D / 5

Since the boat starts following the raft after 9 hours, the total time taken by the boat to catch up to the raft is 9 + (D / 5) hours.

Now, we can equate the distance covered by the boat and the distance covered by the raft to find the value of D.

Distance covered by the boat = Speed of the boat * Time taken by the boat to catch up to the raft Distance covered by the raft = Speed of the raft * Time taken by the boat to catch up to the raft + Distance covered by the raft before the boat started following

Substituting the values, we have: Speed of the boat * (9 + (D / 5)) = Speed of the raft * (9 + 36)

Simplifying the equation, we get: 9 * Speed of the boat + (D / 5) * Speed of the boat = 45 * Speed of the raft + 9 * Speed of the raft

Now, we can solve this equation to find the value of D.

Let's calculate the value of D.

Calculation

Speed of the boat = 9 km/h Speed of the raft = 4 km/h

Substituting the values, we have: 9 * 9 + (D / 5) * 9 = 45 * 4 + 9 * 4

Simplifying the equation, we get: 81 + (D / 5) * 9 = 180 + 36

Subtracting 81 from both sides, we have: (D / 5) * 9 = 135

Dividing both sides by 9, we get: D / 5 = 15

Multiplying both sides by 5, we have: D = 75

Therefore, the boat will catch up to the raft at a distance of 75 km.

Answer

The boat will catch up to the raft at a distance of 75 km.