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. Найдите скорость лодки и скорость катера. составте системы уравнений и решите способом подстановки

Answer 1

Скорость лодки-х
скорост катера-4х
х+1.5*4х=42
7х=42
х=6км/ч

Answer 2

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 was 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.

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.

System of Equations

We can set up a system of equations based on the given information:

Equation 1: Distance = Speed × Time - For the boat: x × 1 = x km - For the motorboat: 4x × 1.5 = 6x km

Equation 2: Total Distance = Distance by Boat + Distance by Motorboat - x + 6x = 42 km

Solution by Substitution

We can solve this system of equations using the method of substitution. Let's solve Equation 2 for x and substitute it into Equation 1 for the boat's speed.

From Equation 2: - x + 6x = 42 - 7x = 42 - x = 6

Substituting x = 6 into Equation 1 for the boat's speed: - Speed of the boat = 6 km/h

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

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

Answer

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