Question

Лодка прошла 34 км по течению реки и 39 км против течения, потратив на это столько времени, сколько ей требуется, чтобы проплыть в стоячей воде 75 км. Найдите отношение скорости лодки в стоячей воде к скорости течения.

Answer 1

Х- скорость течения
скорость лодки-1

34/(1+х)+39/(1-х) = 75
34*(1-х)+39*(1+х) = 75*(1-х²)
34-34х+39+39х = 75-75х²
75х²+5х-2 = 0
D = 25+600 = 625
х = (-5+25)/150 = 20/150 = 2/15
х2(отрицательный)
Скорость течения2/15.
Найдем отношение: 1:2/15 = 1*15/2 = 15:2

Answer 2

Calculation of the Boat's Speed in Still Water

To find the ratio of the boat's speed in still water to the speed of the current, we need to analyze the given information.

According to the problem statement, the boat traveled 34 km downstream (with the current) and 39 km upstream (against the current). Additionally, it took the boat the same amount of time to travel 75 km in still water.

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

To calculate the boat's speed in still water, we can use the formula:

Speed = Distance / Time

1. Downstream Speed: - The boat traveled 34 km downstream, which means it was assisted by the current. - The time taken to cover this distance is the same as the time taken to travel 75 km in still water. - Therefore, the downstream speed is given by: B + C = 34 / T.

2. Upstream Speed: - The boat traveled 39 km upstream, which means it was going against the current. - The time taken to cover this distance is the same as the time taken to travel 75 km in still water. - Therefore, the upstream speed is given by: B - C = 39 / T.

3. Speed in Still Water: - The boat traveled 75 km in still water. - The time taken to cover this distance is the same for both downstream and upstream travel. - Therefore, the speed in still water is given by: B = 75 / T.

Now, we have a system of equations:

B + C = 34 / T (Equation 1) B - C = 39 / T (Equation 2) B = 75 / T (Equation 3)

To solve this system of equations, we can use substitution or elimination.

Let's solve it using substitution:

From Equation 3, we can express B in terms of T:

B = 75 / T

Substituting this value of B into Equations 1 and 2:

75 / T + C = 34 / T (Equation 4) 75 / T - C = 39 / T (Equation 5)

Adding Equations 4 and 5:

2 * (75 / T) = (34 / T) + (39 / T)

Simplifying:

150 / T = 73 / T

Since the denominators are the same, we can equate the numerators:

150 = 73

This is not a valid equation, which means there is no solution for the system of equations. Therefore, the given information is inconsistent, and we cannot determine the ratio of the boat's speed in still water to the speed of the current.

Please note that the given information may contain errors or inconsistencies. It is always important to double-check the problem statement and ensure the information provided is accurate and consistent.

If you have any further questions, please let me know!