Question

Моторная лодка прошла против течения реки 77 км и вернулась в пункт отправления, затратив на обратный путь на 4 часа меньше. Найдите скорость течения,если скорость лодки в неподвижной воде равна 9км/ч. Ответ дайте в км/ч.

Answer 1

Пусть скорость течения Х тогда время против течения  77/(Х-9)   Время по течению 77/(Х+9)  77/(Х-9)-77/(х+9)=4  Отсюда  Х=3км/час

Answer 2

Calculation of River Current Speed

To find the speed of the river current, we can use the formula:

Speed of the river current = (Total distance traveled) / (Total time taken) - (Speed of the boat in still water)

Given information: - Distance traveled against the current = 77 km - Time taken for the return journey = 4 hours less than the time taken for the forward journey - Speed of the boat in still water = 9 km/h

Let's calculate the speed of the river current step by step.

1. Calculate the time taken for the forward journey: - Let's assume the time taken for the forward journey is t hours. - Distance = Speed × Time - Distance traveled against the current = Speed of the boat in still water - Speed of the river current - Distance traveled against the current = (9 km/h - Speed of the river current) × t hours - Distance traveled against the current = 77 km - Therefore, (9 km/h - Speed of the river current) × t = 77 km

2. Calculate the time taken for the return journey: - The time taken for the return journey is 4 hours less than the time taken for the forward journey. - Time taken for the return journey = t - 4 hours

3. Calculate the distance traveled with the current: - Distance traveled with the current = (9 km/h + Speed of the river current) × (t - 4) hours

4. Calculate the total distance traveled: - Total distance traveled = Distance traveled against the current + Distance traveled with the current - Total distance traveled = 77 km + (9 km/h + Speed of the river current) × (t - 4) hours

5. Calculate the total time taken: - Total time taken = Time taken for the forward journey + Time taken for the return journey - Total time taken = t hours + (t - 4) hours

Now, we can substitute the values and solve for the speed of the river current.

Solution:

1. Substitute the values in the equation for the total distance traveled: - 77 km + (9 km/h + Speed of the river current) × (t - 4) hours = (9 km/h - Speed of the river current) × t hours

2. Simplify the equation: - 77 km + 9t - 36 km/h - 4 Speed of the river current = 9t - Speed of the river current × t

3. Rearrange the equation: - 77 km - 36 km/h = -4 Speed of the river current - Speed of the river current × t

4. Simplify further: - 41 km = -5 Speed of the river current - Speed of the river current × t

5. Divide both sides of the equation by -5: - (41 km) / (-5) = Speed of the river current + Speed of the river current × t

6. Simplify: - -8.2 km/h = Speed of the river current + Speed of the river current × t

7. Factor out the Speed of the river current: - -8.2 km/h = Speed of the river current × (1 + t)

8. Solve for the Speed of the river current: - Speed of the river current = -8.2 km/h / (1 + t)

Based on the given information, we don't have the exact value of t (time taken for the forward journey). Therefore, we cannot determine the exact speed of the river current without knowing the value of t.