Question

Туристы на байдарке плыли 2,4 ч. по течению реки и 1,8 ч. против течения. Путь который байдарка проплыла по течению , был на 14,1км больше ,чем путь пройденный против течения .Найдите скорость байдарки в стоячей воде ,если скорость течения 2,5 км/ч.

Answer 1

Пусть х=скорость бойдарки, тогда х+2,3 по теч реки, а ч-2,3 против. известно, что Туристы на байдарке плыли 2,4 ч. по течению реки и 1,8 ч. против течения, Путь который байдарка проплыла по течению , был на 14,1км больше ,чем путь пройденный против течения . Составим и решим ураавнение: (х+2,3)*2,4-(х-2,3)*1,8=14,1 2,4х+5,52-1,8х+4,14=14,1 0,6х+9,66=14,1 0,6х=14,1-9,66 0,6х=4,44 х=4,44/0,6 х=7,4 Ответ 7,4 км/ч

Answer 2

Problem Analysis

We are given that a kayak traveled for 2.4 hours downstream and 1.8 hours upstream on a river. The distance covered downstream is 14.1 km more than the distance covered upstream. We need to find the speed of the kayak in still water, given that the speed of the current is 2.5 km/h.

Solution

Let's assume the speed of the kayak in still water is x km/h.

When the kayak is traveling downstream, its effective speed is the sum of its speed in still water and the speed of the current. Therefore, the distance covered downstream can be calculated as (x + 2.5) * 2.4 km.

When the kayak is traveling upstream, its effective speed is the difference between its speed in still water and the speed of the current. Therefore, the distance covered upstream can be calculated as (x - 2.5) * 1.8 km.

According to the problem, the distance covered downstream is 14.1 km more than the distance covered upstream. So we can set up the following equation:

(x + 2.5) * 2.4 = (x - 2.5) * 1.8 + 14.1

Now we can solve this equation to find the value of x.

Calculation

Let's solve the equation step by step:

(x + 2.5) * 2.4 = (x - 2.5) * 1.8 + 14.1

Expanding the equation:

2.4x + 6 = 1.8x - 4.5 + 14.1

Combining like terms:

2.4x - 1.8x = 14.1 - 4.5 - 6

Simplifying:

0.6x = 3.6

Dividing both sides by 0.6:

x = 3.6 / 0.6

Calculating:

x = 6

Answer

The speed of the kayak in still water is 6 km/h.

Verification

Let's verify the answer by substituting the value of x into the equation:

(6 + 2.5) * 2.4 = (6 - 2.5) * 1.8 + 14.1

Simplifying:

8.5 * 2.4 = 3.5 * 1.8 + 14.1

Calculating:

20.4 = 6.3 + 14.1

20.4 = 20.4

The equation is balanced, which means our answer is correct.

Conclusion

The speed of the kayak in still water is 6 km/h.