Question

ТЕПЛОХОД ПРОХОДИТ ПО ТЕЧЕНИЮ ДО ПУНКТА 126 КМ и после стоянки возвращается в пункт отправления.Найдите собственную скорость теплохода,если скорость течения равна 2 км/ч ,стоянка длится 8 часов , а в пункт отправления теплоход возвращается ровно через сутки после отплытия из него .Дайте ответ и решение в км/ч

Answer 1

X скорость теплохода
x-2 скорость против течения
x+2 скорость по течению
S=VT
T=S/V
126/(v+2) - время до пункта по течению
126/(v-2)  - время обратно домой против течения 
24 время туда обратно стоянка
126/(v+2)+126/(v-2)+8=24
126/(v+2)+126/(v-2)=16
63(v-2)+63(v+2)=8
63v-126+63v+126=8(v-2)(v+2)
2*63v=8(v²-4)
8v²-126v-32=0
D=126+4*8*32=130*130
t12=(126+-130)/16= -1/4 16
-1/4 скорость не может быть отрицательной
x=16 км час
126/18+126/14+8=8+7+9=24

Answer 2

Problem Analysis

We are given the following information: - A boat travels with the current to a point 126 km away and then returns to the starting point after an 8-hour stop. - The current has a speed of 2 km/h. - The boat returns exactly 24 hours after departing from the starting point.

We need to find the speed of the boat.

Solution

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

When the boat is traveling with the current, its effective speed is the sum of its own speed and the speed of the current. So, the effective speed is (v + 2) km/h.

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

We can calculate the time taken for the boat to travel to the point 126 km away and return to the starting point using the formula:

time = distance / speed

The time taken to travel to the point 126 km away is:

time1 = 126 / (v + 2)

The time taken to return to the starting point is:

time2 = 126 / (v - 2)

According to the given information, the boat returns exactly 24 hours after departing from the starting point. So, the total time taken for the round trip is:

time1 + time2 + 8 = 24

Substituting the values of time1 and time2, we get:

126 / (v + 2) + 126 / (v - 2) + 8 = 24

Simplifying the equation, we can solve for v.

Calculation

Let's solve the equation to find the value of v.

126 / (v + 2) + 126 / (v - 2) + 8 = 24

Multiplying through by (v + 2)(v - 2) to eliminate the denominators:

126(v - 2) + 126(v + 2) + 8(v + 2)(v - 2) = 24(v + 2)(v - 2)

Expanding and simplifying:

126v - 252 + 126v + 252 + 8(v^2 - 4) = 24(v^2 - 4)

252v + 8v^2 - 1008 = 24v^2 - 96

16v^2 - 252v - 912 = 0

Dividing through by 4 to simplify:

4v^2 - 63v - 228 = 0

Using the quadratic formula:

v = (-b ± √(b^2 - 4ac)) / (2a)

where a = 4, b = -63, and c = -228.

Solving for v, we get two possible values: v ≈ 15.75 km/h and v ≈ -3.75 km/h.

Since the speed of the boat cannot be negative, the speed of the boat is approximately 15.75 km/h.

Answer

The speed of the boat is approximately 15.75 km/h.