Question

Помогите решить задачу! Катер за 2 часа 40 мин, проплывает по течению реки 48 км, а против течения за 3 часа на 6 км меньше. Найдите скорость течения реки, и скорость катера.

Answer 1

48-6:3=14(км/ч)-против течения
48:400*60=7,2(км/ч)-по течению
14-7,2=6,8(км/ч)-течение
7,2-6,8=0,4(км/ч)-скорость катера

Answer 2

Problem Analysis

To solve this problem, we need to find the speed of the river current and the speed of the boat. We are given the time it takes for the boat to travel a certain distance both with and against the current. By using the formula distance = speed × time, we can set up a system of equations to solve for the unknowns.

Let's assume the speed of the boat is represented by b and the speed of the river current is represented by c.

Solution

1. We are given that the boat takes 2 hours and 40 minutes (or 2.67 hours) to travel 48 km with the current. Using the formula distance = speed × time, we can write the equation: 48 = (b + c) × 2.67.

2. We are also given that the boat takes 3 hours to travel 6 km less than the distance traveled with the current. Using the formula distance = speed × time, we can write the equation: 48 - 6 = (b - c) × 3.

Now we have a system of two equations with two unknowns. We can solve this system to find the values of b and c.

Let's solve the system of equations:

Solving the System of Equations

1. Rearrange the first equation to isolate b + c: 48 = 2.67(b + c) Divide both sides by 2.67: 18 = b + c

2. Rearrange the second equation to isolate b - c: 42 = 3(b - c) Divide both sides by 3: 14 = b - c

Now we have a system of two equations: 18 = b + c 14 = b - c

We can solve this system of equations using the method of substitution or elimination.

Method 1: Substitution

1. Solve the second equation for b in terms of c: 14 = b - c Add c to both sides: 14 + c = b

2. Substitute this expression for b into the first equation: 18 = (14 + c) + c Simplify: 18 = 14 + 2c Subtract 14 from both sides: 4 = 2c Divide both sides by 2: 2 = c

3. Substitute the value of c back into the second equation to find b: 14 = b - 2 Add 2 to both sides: 16 = b

Therefore, the speed of the river current is 2 km/h and the speed of the boat is 16 km/h.

Method 2: Elimination

1. Add the two equations together to eliminate c: 18 + 14 = (b + c) + (b - c) Simplify: 32 = 2b Divide both sides by 2: 16 = b

2. Substitute the value of b back into the first equation to find c: 18 = 16 + c Subtract 16 from both sides: 2 = c

Therefore, the speed of the river current is 2 km/h and the speed of the boat is 16 km/h.

Conclusion

The speed of the river current is 2 km/h and the speed of the boat is 16 km/h.