Question

Лодка плыла те­че­нию 4 часа, а затем 5 часов про­тив те­че­ния, прой­дя всего 115 км. Най­ди­те соб­ствен­ную ско­рость лодки, если из­вест­но, что ско­рость те­че­ния реки равна 2 км/ч.

Answer 1

Пусть х км/ч-скорость лодки, тогда
4(х+2)+5(х-2)=115
4х+8+5х-10=115
9х=117
х=13; значит скорость лодки 13 км/ч
Ответ: 13км/ч

Answer 2

Problem Analysis

We are given that a boat traveled with the current for 4 hours and then against the current for 5 hours, covering a total distance of 115 km. The speed of the current is given as 2 km/h. We need to find the speed of the boat.

Solution

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

When the boat is traveling with the current, its effective speed is the sum of its speed in still water and the speed of the current. So, the effective speed is (x + 2) km/h.

When the boat is traveling against the current, its effective speed is the difference between its speed in still water and the speed of the current. So, the effective speed is (x - 2) km/h.

We can use the formula distance = speed × time to calculate the distances traveled in each case.

The distance traveled with the current for 4 hours is (x + 2) × 4 km.

The distance traveled against the current for 5 hours is (x - 2) × 5 km.

According to the problem, the total distance traveled is 115 km. So, we can set up the equation:

(x + 2) × 4 + (x - 2) × 5 = 115

Simplifying the equation:

4x + 8 + 5x - 10 = 115

9x - 2 = 115

9x = 117

x = 13

Therefore, the speed of the boat in still water is 13 km/h.

Answer

The speed of the boat in still water is 13 km/h.