Question

туристы плыли на лодке 1 час, а на катере- 1,5 часа. всего они проплыли 42 км. скорость катера в 4 раза больше, чем скорость лодки.найди скорость лодки и скорость катера. способом решении системы

Answer 1

Problem Analysis

We are given that tourists traveled on a boat for 1 hour and on a motorboat for 1.5 hours. The total distance traveled is 42 km, and the speed of the motorboat is 4 times greater than the speed of the boat. We need to find the speed of the boat and the speed of the motorboat.

Solution

Let's assume the speed of the boat is x km/h. Since the speed of the motorboat is 4 times greater, the speed of the motorboat is 4x km/h.

We can use the formula distance = speed × time to create two equations based on the given information.

For the boat: x km/h × 1 hour = distance

For the motorboat: 4x km/h × 1.5 hours = distance

Since the total distance traveled is 42 km, we can set up the following equation: x km/h × 1 hour + 4x km/h × 1.5 hours = 42 km

Now we can solve this equation to find the values of x and 4x.

Calculation

Let's solve the equation:

x km/h × 1 hour + 4x km/h × 1.5 hours = 42 km

Simplifying the equation:

x + 6x = 42

Combining like terms:

7x = 42

Dividing both sides by 7:

x = 6

So the speed of the boat is 6 km/h.

Since the speed of the motorboat is 4 times greater, the speed of the motorboat is 4 × 6 = 24 km/h.

Answer

The speed of the boat is 6 km/h and the speed of the motorboat is 24 km/h.

Please let me know if you need any further assistance!