Question

Теп­ло­ход про­хо­дит по те­че­нию реки до пунк­та на­зна­че­ния 399 км и после сто­ян­ки воз­вра­ща­ет­ся в пункт от­прав­ле­ния. Най­ди­те ско­рость те­че­ния, если ско­рость теп­ло­хо­да в не­по­движ­ной воде равна 20 км/ч, сто­ян­ка длит­ся 2 часа, а в пункт от­прав­ле­ния теп­ло­ход воз­вра­ща­ет­ся через 42 часа после от­плы­тия из него. Ответ дайте в км/ч.

Answer 1

Ответ:

1 км/ч .

Объяснение:

Пусть х км/ч - скорость течения. Тогда (20+х) км/ч - скорость по течению реки, а ( 20-х) км/ч - скорость против течения реки.

$\dfrac{399}{20+x}$  ч- время, затраченное на путь по течению

$\dfrac{399}{20-x}$  ч- время, затраченное на путь против течения.

Всего теплоход был в пути 42-2=40 ч.

Составим уравнение:

$\dfrac{399}{20+x}+\dfrac{399}{20-x}=40|\cdot(20+x)(20-x) ;\\\\\dfrac{399}{20+x}^{\backslash(20-x)}+\dfrac{399}{20-x}^{\backslash(20+x)}=40^{\backslash(20-x)(20+x)};\\\\\ 399\cdot(20-x)+399\cdot(20+x)=40\cdot(400-x^{2} );\\399\cdot20-399x+399\cdot20+399x=40\cdot(400-x^{2} );\\399\cdot40=40\cdot(400-x^{2} )|:40;\\399=400-x^{2} ;\\x^{2} =400-399;\\x^{2} =1;\\x{_1}=-1;\\x{_2}=2$

Так как скорость не может быть отрицательным числом, то скорость течения равна 1 км/ч.

Answer 2

Calculation of the River's Current Speed

To find the speed of the river's current, we need to consider the round trip of the boat. Let's break down the given information:

- Distance traveled to the destination: 399 km - Speed of the boat in still water: 20 km/h - Duration of the stop at the destination: 2 hours - Duration of the round trip: 42 hours after departure from the starting point

To calculate the speed of the river's current, we can use the formula:

Speed of the boat in still water = Speed of the current + Speed of the boat against the current

Since the boat travels both downstream and upstream, we need to consider the effects of the current in both directions.

Let's assume the speed of the river's current is represented by 'x' km/h.

1. Downstream Journey: - Speed of the boat relative to the current: 20 km/h + x km/h - Time taken for the downstream journey: 399 km / (20 km/h + x km/h)

2. Upstream Journey: - Speed of the boat relative to the current: 20 km/h - x km/h - Time taken for the upstream journey: 399 km / (20 km/h - x km/h)

3. Total Time for the Round Trip: - Total time = Time for downstream journey + Time for upstream journey + Duration of stop at the destination - 42 hours = 399 km / (20 km/h + x km/h) + 399 km / (20 km/h - x km/h) + 2 hours

Now, we can solve this equation to find the value of 'x', which represents the speed of the river's current.

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