Question

Теплоход за 7 часов проходит такой же путь как катер за 4 часа. Найдите скорость теплохода, если она меньше скорости катера на 24 км/ч

Answer 1

пусть скорость теплохода х км/ч. значит скорость катера 24+х кмч. расстояние, которое прошел теплоход х*7, а катер (х+24)*4. но по условию задачи расстояние было одинаковое. составим и решим уравнение

7х=4*(х+24)

7х=4х+ 96

3х=96

х=32

ответ 32 км/ч скорость теплохода 

 

Answer 2

7x=4x+24
7x-4x=24
3x=24
x=24:3
x=8
Ответ : скорость теплохода 32 км/ч.

Answer 3

Problem Analysis

We are given that a steamboat covers the same distance in 7 hours as a motorboat covers in 4 hours. We need to find the speed of the steamboat, given that it is 24 km/h slower than the speed of the motorboat.

Solution

Let's assume the speed of the motorboat is x km/h. According to the problem, the steamboat covers the same distance in 7 hours as the motorboat covers in 4 hours.

We can use the formula distance = speed × time to calculate the distance covered by both the steamboat and the motorboat.

For the steamboat: - Speed = (x - 24) km/h (since it is 24 km/h slower than the motorboat) - Time = 7 hours

For the motorboat: - Speed = x km/h - Time = 4 hours

Since the distances covered by both boats are the same, we can set up the equation:

(x - 24) × 7 = x × 4

Now, let's solve this equation to find the value of x.

Calculation

Expanding the equation, we get:

7x - 168 = 4x

Simplifying the equation, we get:

7x - 4x = 168

3x = 168

Dividing both sides of the equation by 3, we get:

x = 56

Answer

The speed of the motorboat, x, is 56 km/h. Therefore, the speed of the steamboat is (x - 24) = 56 - 24 = 32 km/h.

So, the speed of the steamboat is 32 km/h.

Verification

Let's verify our answer using the given information.

According to the problem, the steamboat covers the same distance in 7 hours as the motorboat covers in 4 hours. Let's calculate the distance covered by both boats and check if they are the same.

For the steamboat: - Speed = 32 km/h - Time = 7 hours - Distance = Speed × Time = 32 km/h × 7 hours = 224 km

For the motorboat: - Speed = 56 km/h - Time = 4 hours - Distance = Speed × Time = 56 km/h × 4 hours = 224 km

As we can see, both boats cover the same distance of 224 km. Therefore, our answer is verified.

Conclusion

The speed of the steamboat is 32 km/h.