Question

Теплоход, скорость которого в неподвижной воде равна 20 км/ч, проходит по течению реки и после стоянки возвращается в исходный пункт. Скорость течения равна 4 км/ч, стоянка длится 4 часа, а в исходный пункт теплоход возвращается через 14 часов после отплытия из него. Сколько километров прошел теплоход за весь рейс?

Answer 1

$\frac{x}{20+4} + \frac{x}{20-4} =14-4 \\ \frac{x}{24} + \frac{x}{16} =10 /*48 \\ 2x+3x=480 \\ 5x=480 \\ x=480:5 \\ x=96 \\ 96*2=192$
км прошел теплоход за весь рейс

Answer 2

Calculation of the Distance Traveled by the Boat

To calculate the distance traveled by the boat for the entire journey, we need to consider the boat's speed in still water, the speed of the river's current, the duration of the stop, and the time taken to return to the starting point.

Let's break down the given information:

- Speed of the boat in still water: 20 km/h- Speed of the river's current: 4 km/h- Duration of the stop: 4 hours - Time taken to return to the starting point: 14 hours after departure

To calculate the distance traveled, we can use the formula:

Distance = Speed x Time

First, let's calculate the distance traveled by the boat while moving with the current:

Distance1 = (Speed of the boat + Speed of the current) x Time1

Substituting the given values:

Distance1 = (20 km/h + 4 km/h) x (14 hours - 4 hours)

Simplifying:

Distance1 = 24 km/h x 10 hours

Distance1 = 240 km

Next, let's calculate the distance traveled by the boat while moving against the current:

Distance2 = (Speed of the boat - Speed of the current) x Time2

Substituting the given values:

Distance2 = (20 km/h - 4 km/h) x 14 hours

Simplifying:

Distance2 = 16 km/h x 14 hours

Distance2 = 224 km

Finally, to calculate the total distance traveled for the entire journey, we add the distances traveled in each direction:

Total Distance = Distance1 + Distance2

Total Distance = 240 km + 224 km

Total Distance = 464 km

Therefore, the boat traveled a total distance of 464 kilometers for the entire journey.