Question

Теп­ло­ход про­хо­дит по те­че­нию реки до пунк­та на­зна­че­ния 391 км и после сто­ян­ки воз­вра­ща­ет­ся в пункт от­прав­ле­ния. Най­ди­те ско­рость теп­ло­хо­да в не­по­движ­ной воде, если ско­рость те­че­ния равна 3 км/ч, сто­ян­ка длит­ся 6 часов, а в пункт от­прав­ле­ния теп­ло­ход воз­вра­ща­ет­ся через 46 часов после от­плы­тия из него. Ответ дайте в км/ч.

Answer 1

Пусть х- скорость теплохода км/ч
х+3- скорость теплохода по течению
х-3-скорость теплохода против течения
1) 46-6=40(ч)-время движения
391:(х+3)+391:(х-3)=40
391(х-3)+391(х+3)=40(х-3)(х+3)
391х-1173+391х+1173=40(х^2-9)
782х=40х^2-360=0
40х^2-391х-180=0
D=152881+14400=167281=409^2
x1=(391-409):40=18:40=-0,45<0
х2=(391+409):40=800:40=20(км/ч)-скорость теплохода в неподвижной воде
ОТВЕТ-20 км/ч
ОТМЕТЬ КАК ЛУЧШИЙ

Answer 2

Calculation of the Speed of the Boat

To find the speed of the boat in still water, we need to consider the following information:

- Distance traveled to the destination: 391 km - Speed of the river current: 3 km/h - Duration of the stop at the destination: 6 hours - Duration of the return journey from the destination: 46 hours

Let's break down the problem into two parts: the journey to the destination and the return journey.

# Journey to the Destination

During the journey to the destination, the boat is moving against the current. This means that the effective speed of the boat is reduced by the speed of the current. We can calculate the time taken for this journey using the formula:

Time = Distance / Speed

Let's denote the speed of the boat in still water as B.

The effective speed of the boat during the journey to the destination is given by:

Effective Speed = B - Speed of Current

Using the formula for time, we can write:

Time to Destination = Distance / Effective Speed

Substituting the given values, we have:

Time to Destination = 391 km / (B - 3 km/h)

# Return Journey from the Destination

During the return journey, the boat is moving with the current. This means that the effective speed of the boat is increased by the speed of the current. We can calculate the time taken for this journey using the same formula as before:

Time = Distance / Speed

The effective speed of the boat during the return journey is given by:

Effective Speed = B + Speed of Current

Using the formula for time, we can write:

Time from Destination = Distance / Effective Speed

Substituting the given values, we have:

Time from Destination = 391 km / (B + 3 km/h)

# Total Time

The total time for the round trip is the sum of the time to the destination, the stop at the destination, and the time from the destination. We can write:

Total Time = Time to Destination + Stop Time + Time from Destination

Substituting the given values, we have:

Total Time = 391 km / (B - 3 km/h) + 6 hours + 391 km / (B + 3 km/h)

# Solving for the Speed of the Boat

To find the speed of the boat in still water, we need to solve the equation for the total time. However, this equation involves a quadratic term, which makes it difficult to solve directly. We can simplify the equation by multiplying both sides by the denominators and rearranging the terms:

Total Time * (B - 3 km/h) * (B + 3 km/h) = 391 km * (B + 3 km/h) + 6 hours * (B - 3 km/h)

Expanding and simplifying the equation, we get:

Total Time * (B^2 - 9 km^2/h^2) = 391 km * B + 1173 km^2/h + 6 hours * (B - 3 km/h)

Converting the stop time from hours to km by multiplying by the speed of the boat, we have:

Total Time * (B^2 - 9 km^2/h^2) = 391 km * B + 1173 km^2/h + 6 hours * B - 18 km

Combining like terms, we get:

Total Time * B^2 - 9 km^2/h^2 * Total Time = 397 km * B + 1173 km^2/h - 18 km

Rearranging the equation, we have:

Total Time * B^2 - 397 km * B - 9 km^2/h^2 * Total Time - 1173 km^2/h + 18 km = 0

This is a quadratic equation in terms of the speed of the boat, B. We can solve this equation to find the value of B.

Unfortunately, without the specific value of the total time, we cannot provide an exact answer for the speed of the boat in still water. If you have the value of the total time, please provide it, and we can solve the equation to find the speed of the boat.