Question

Відстань між двома пристанями теплохід проходить за 2год 30хв. Якщо швидкість теплохода зменшити на 6 км/год, то на цей шлях теплохід витратить 3год 15 хв. Знайдить початкову швидкисть теплохода

Answer 1

Позначим швидкість теплохода за v.

2 год. 30 хв. = $2 \frac{1}{2}$ год.
3 год. 15 хв. = $3 \frac{1}{4}$ год.

Складемо рівняння:
$v*2 \frac{1}{2}=(v-6)*3 \frac{1}{4} \\ v*\frac{5}{2}=(v-6)*\frac{13}{4}\\v*10=(v-6)*13$
10v = 13v - 78
3v = 78
v = 26 км/год

Answer 2

Problem Analysis

We are given that a steamship travels between two ports in 2 hours and 30 minutes. If the speed of the steamship is reduced by 6 km/h, it takes 3 hours and 15 minutes to cover the same distance. We need to find the initial speed of the steamship.

Solution

Let's assume the initial speed of the steamship is v km/h.

We can use the formula: Distance = Speed × Time.

According to the problem, when the steamship travels at the initial speed, it takes 2 hours and 30 minutes to cover the distance. Converting this time to hours, we have:

Time1 = 2 hours + 30 minutes = 2.5 hours

Similarly, when the speed of the steamship is reduced by 6 km/h, it takes 3 hours and 15 minutes to cover the same distance. Converting this time to hours, we have:

Time2 = 3 hours + 15 minutes = 3.25 hours

Let's denote the distance between the two ports as d km.

Using the formula Distance = Speed × Time, we can write two equations based on the given information:

Equation 1: d = v × 2.5 (when the speed is v km/h)

Equation 2: d = (v - 6) × 3.25 (when the speed is reduced by 6 km/h)

Now, we can solve these two equations to find the initial speed of the steamship.

Solving the Equations

Let's solve the equations step by step:

Equation 1: d = v × 2.5

Equation 2: d = (v - 6) × 3.25

Since both equations are equal to d, we can equate them:

v × 2.5 = (v - 6) × 3.25

Expanding the equation:

2.5v = 3.25v - 19.5

Rearranging the terms:

3.25v - 2.5v = 19.5

0.75v = 19.5

Dividing both sides by 0.75:

v = 19.5 / 0.75

v = 26

Therefore, the initial speed of the steamship is 26 km/h.

Conclusion

The initial speed of the steamship is 26 km/h.