Question

79.Катер шел по течению реки 5 ч, а затем против течения 3 ч. Найдите собственную скорость катера, если известно, что скорость течения реки 3 км/ч, а всего пройдено 126 км 80.Из пункта М в пункт N выехал автобус. Через полчаса из N в М со скоростью, превышающей скорость автобуса на 18 км/ч, выехал легковой автомобиль. Через 1 ч 20 мин после своего выхода он встретил автобус, причем проехал расстояние, на3 км большее, чем автобус. Чему равно расстояние между М и N?

Answer 1

Task 79: Катер шел по течению реки 5 ч, а затем против течения 3 ч. Найдите собственную скорость катера, если известно, что скорость течения реки 3 км/ч, а всего пройдено 126 км.

To find the speed of the boat, we can use the formula:

Speed of boat = (Total distance traveled) / (Total time taken)

Let's calculate the speed of the boat step by step:

1. The boat traveled downstream for 5 hours. During this time, it covered a distance equal to the speed of the boat plus the speed of the river current multiplied by the time taken. So, the distance traveled downstream is:

Distance downstream = (Speed of boat + Speed of current) × Time downstream

Substituting the given values: Distance downstream = (Speed of boat + 3 km/h) × 5 h

2. The boat then traveled upstream for 3 hours. During this time, it covered a distance equal to the speed of the boat minus the speed of the river current multiplied by the time taken. So, the distance traveled upstream is:

Distance upstream = (Speed of boat - Speed of current) × Time upstream

Substituting the given values: Distance upstream = (Speed of boat - 3 km/h) × 3 h

3. The total distance traveled by the boat is given as 126 km. So, we can write the equation:

Distance downstream + Distance upstream = Total distance

Substituting the calculated values: (Speed of boat + 3 km/h) × 5 h + (Speed of boat - 3 km/h) × 3 h = 126 km

Now, let's solve this equation to find the speed of the boat.

Solution:

Let's simplify the equation:

(5(Speed of boat) + 15 km/h) + (3(Speed of boat) - 9 km/h) = 126 km

Combining like terms:

8(Speed of boat) + 6 km/h = 126 km

Subtracting 6 km/h from both sides:

8(Speed of boat) = 120 km

Dividing both sides by 8:

Speed of boat = 15 km/h

Therefore, the speed of the boat is 15 km/h.