Question

Собственная скорость моторной лодки 8 км/ч. Скорость течения реки 1 2/5 км. Лодка шла два часа против течения реки и 2 часа по течению реки. Какой путь прошла моторная лодка за эти 4 часа?(пожалуйста можно без десятичных дробей)

Answer 1

1) 8 - 1 2/5 = 40/5 - 7/5 = 33/5 = 6 3/5 км/ч - скорость против течения,
2) 8 + 1 2/5 = 9 2/5 км/ч - скорость по течению,
3) 6 3/5 * 2 = 13 1/5 км - расстояние против течени,
4) 9 2/5 * 2 = 18 4/5 км - расст. по течению,
5) 13 1/5 + 18 4/5 = 32 км.

ответ: моторная лодка прошла 32 км

Answer 2

Problem Analysis

To solve this problem, we need to calculate the distance traveled by the motorboat in 4 hours. The motorboat traveled for 2 hours against the current of the river and 2 hours with the current of the river. We are given the speed of the motorboat and the speed of the river's current. We can use the formula: distance = speed × time to calculate the distance traveled in each direction and then add them together to get the total distance traveled.

Calculation

Given: - Speed of the motorboat = 8 km/h - Speed of the river's current = 1 2/5 km/h

To calculate the distance traveled against the current: - Speed of the motorboat relative to the river's current = Speed of the motorboat - Speed of the river's current - Time traveled against the current = 2 hours - Distance traveled against the current = Speed of the motorboat relative to the river's current × Time traveled against the current

To calculate the distance traveled with the current: - Speed of the motorboat relative to the river's current = Speed of the motorboat + Speed of the river's current - Time traveled with the current = 2 hours - Distance traveled with the current = Speed of the motorboat relative to the river's current × Time traveled with the current

To calculate the total distance traveled: - Total distance traveled = Distance traveled against the current + Distance traveled with the current

Let's calculate the distances step by step.

Calculation of Distance Traveled Against the Current

Speed of the motorboat relative to the river's current = Speed of the motorboat - Speed of the river's current = 8 km/h - 1 2/5 km/h

To subtract fractions, we need a common denominator. The common denominator for 5 and 2 is 10.

= 8 km/h - (7/5) km/h = (40/5) km/h - (7/5) km/h = (40 - 7)/5 km/h = 33/5 km/h

Distance traveled against the current = Speed of the motorboat relative to the river's current × Time traveled against the current = (33/5) km/h × 2 hours = (33 × 2)/(5 × 1) km = 66/5 km

Calculation of Distance Traveled With the Current

Speed of the motorboat relative to the river's current = Speed of the motorboat + Speed of the river's current = 8 km/h + 1 2/5 km/h

To add fractions, we need a common denominator. The common denominator for 5 and 2 is 10.

= 8 km/h + (7/5) km/h = (40/5) km/h + (7/5) km/h = (40 + 7)/5 km/h = 47/5 km/h

Distance traveled with the current = Speed of the motorboat relative to the river's current × Time traveled with the current = (47/5) km/h × 2 hours = (47 × 2)/(5 × 1) km = 94/5 km

Calculation of Total Distance Traveled

Total distance traveled = Distance traveled against the current + Distance traveled with the current = (66/5) km + (94/5) km = (66 + 94)/5 km = 160/5 km = 32 km

Answer

The motorboat traveled a distance of 32 km in the 4 hours.

Calculation Verification

Let's verify the calculation using the given information.

The motorboat traveled for 2 hours against the current at a speed of 8 km/h. Therefore, the distance traveled against the current is 2 hours × 8 km/h = 16 km.

The motorboat also traveled for 2 hours with the current at a speed of 8 km/h. Therefore, the distance traveled with the current is 2 hours × 8 km/h = 16 km.

The total distance traveled is 16 km + 16 km = 32 km, which matches our calculated result.

Therefore, the motorboat traveled a distance of 32 km in the 4 hours, which is consistent with the given information.

Conclusion

The motorboat traveled a distance of 32 km in the 4 hours.