Question

Два теплохода, двигаясь по реке навстречу друг другу, встретились через 4 часа. Скорость течения реки равна 1,5 км/час. Через сколько часов встретились бы эти теплоходы, если б скорость течения реки была бы в 2,2 раза больше. помогите пожалуйста

Answer 1

Они бы встретились через 4 часа.
В таких задачах, где 2 судна плывут навстречу друг другу, скорость течения можно просто опускать, так как к скорости одного это + скорость течения, а к скорости второго это - скорость течения. То на то и выходит.

Удачи)

Answer 2

Problem Analysis

We are given two boats moving towards each other on a river. The time it takes for them to meet is given, as well as the speed of the river's current. We need to determine how long it would take for the boats to meet if the speed of the river's current were 2.2 times greater.

Solution

Let's denote the speed of the first boat as x km/h and the speed of the second boat as y km/h. The speed of the river's current is given as 1.5 km/h.

When the boats are moving towards each other, their effective speeds are increased by the speed of the river's current. Therefore, the effective speed of the first boat is (x + 1.5) km/h, and the effective speed of the second boat is (y + 1.5) km/h.

We are given that the boats meet after 4 hours. Using the formula distance = speed × time, we can calculate the distance traveled by each boat:

- Distance traveled by the first boat = (x + 1.5) × 4 km - Distance traveled by the second boat = (y + 1.5) × 4 km

Since the boats are moving towards each other, the sum of their distances traveled should be equal to the total distance between them. Therefore, we can set up the following equation:

(x + 1.5) × 4 + (y + 1.5) × 4 = d,

where d is the total distance between the boats.

Now, let's consider the scenario where the speed of the river's current is 2.2 times greater. In this case, the effective speed of the first boat would be (x + 2.2 × 1.5) km/h, and the effective speed of the second boat would be (y + 2.2 × 1.5) km/h.

We want to find the time it takes for the boats to meet in this scenario. Let's denote this time as t hours. Using the same formula as before, we can calculate the distance traveled by each boat:

- Distance traveled by the first boat = (x + 2.2 × 1.5) × t km - Distance traveled by the second boat = (y + 2.2 × 1.5) × t km

Since the boats are moving towards each other, the sum of their distances traveled should be equal to the total distance between them. Therefore, we can set up the following equation:

(x + 2.2 × 1.5) × t + (y + 2.2 × 1.5) × t = d.

Now, we can solve these two equations simultaneously to find the value of t.

Calculation

Let's solve the equations using the given values:

(x + 1.5) × 4 + (y + 1.5) × 4 = d,

(x + 2.2 × 1.5) × t + (y + 2.2 × 1.5) × t = d.

Substituting the given values, we have:

(x + 1.5) × 4 + (y + 1.5) × 4 = d,

(x + 2.2 × 1.5) × t + (y + 2.2 × 1.5) × t = d.

Simplifying the equations, we get:

4x + 4y + 12 = d,

t(x + 3.3) + t(y + 3.3) = d.

Since the total distance between the boats is the same in both scenarios, we can equate the two equations:

4x + 4y + 12 = t(x + 3.3) + t(y + 3.3).

Simplifying further, we have:

4x + 4y + 12 = tx + 3.3t + ty + 3.3t.

Rearranging the terms, we get:

4x + 4y + 12 = (x + y)t + 6.6t.

Since the equation holds true for any values of x, y, and t, we can equate the coefficients of the variables on both sides:

4 = t + 6.6,

which simplifies to:

t = 4 - 6.6,

t = -2.6.

However, a negative time value does not make sense in this context. Therefore, we can conclude that the boats would not meet if the speed of the river's current were 2.2 times greater.

Answer

If the speed of the river's current were 2.2 times greater, the boats would not meet.