Question

За 2 часа моторная лодка прошла по течению реки 68 км, а за 2 часа против течения расстояние на 8 км меньше. Во сколько раз скорость лодки по течению больше скорости течения реки?

Answer 1

1).68/2=34 км/ч -скорость по течению реки

2). 68-8=60км -путь против течения

3).60/2=30 км/ч -скорость против течения

4). (34-30)/2=2 км/ч -скорость течения реки.

5). 34/2=17 в 17 раз

Answer 2

Х+2 - скорость по течению
х-2 - скорость против течения

2*(х+2) = 68
2х+4 = 68
2х = 64
х = 32

х+2 = 34 км/час - скорость по течению
х-2 = 30 км/час - скорость против течения

34/2 = 17

Ответ: в 17 раз

Answer 3

Problem Analysis

We are given that a motorboat traveled a distance of 68 km downstream in 2 hours, and the same distance upstream in 2 hours, but the upstream distance is 8 km less than the downstream distance. We need to determine the ratio of the boat's speed relative to the current to the speed of the current.

Solution

Let's assume the speed of the boat in still water is B km/h, and the speed of the current is C km/h.

When the boat is traveling downstream, its effective speed is the sum of the boat's speed in still water and the speed of the current. So, the effective speed downstream is B + C km/h.

When the boat is traveling upstream, its effective speed is the difference between the boat's speed in still water and the speed of the current. So, the effective speed upstream is B - C km/h.

We are given that the boat traveled a distance of 68 km downstream in 2 hours, and the same distance upstream in 2 hours, but the upstream distance is 8 km less than the downstream distance. This can be expressed as:

Downstream distance = 68 km Upstream distance = 68 km - 8 km = 60 km

Using the formula distance = speed × time, we can write the following equations:

Downstream: (B + C) × 2 = 68 Upstream: (B - C) × 2 = 60

Let's solve these equations to find the values of B and C.

Calculation

We can solve the equations using the method of substitution or elimination. Let's use the method of substitution.

From the downstream equation, we have: B + C = 68/2 B + C = 34

From the upstream equation, we have: B - C = 60/2 B - C = 30

Now, we can solve these two equations simultaneously to find the values of B and C.

Adding the two equations together, we get: 2B = 34 + 30 2B = 64 B = 64/2 B = 32

Substituting the value of B back into one of the equations, we can solve for C: 32 - C = 30 C = 32 - 30 C = 2

Answer

Therefore, the speed of the boat in still water is 32 km/h, and the speed of the current is 2 km/h. To find the ratio of the boat's speed relative to the current to the speed of the current, we divide the speed of the boat in still water by the speed of the current:

32 km/h / 2 km/h = 16

So, the speed of the boat relative to the current is 16 times greater than the speed of the current.

Conclusion

The speed of the boat relative to the current is 16 times greater than the speed of the current.