Question

Со станции м до станции N выехал электропоезд со скоростью 60 км/ч, а через 10 мин за ним со станции М выехал второй электропоезд, скорость которого 85 км/ч. На каком расстоянии до станции N второй электропоезд догонит первый, если расстояние между пунктами 40км.

Answer 1

Найдем расстояние на которое уехал 1 э/п за 10 минут
10 мин = 1/6 часа
60*1/6=10 км
вспомним формулу для движения вдогонку $S=(v_1-v_2)*t$
когда выехал 2 э/п расстояние между ними было 10 км
(85-60)*t=10
25*t=10
t=0,4 часа - догонит 2 э/п
найдем какое расстояние пройдет за это время 1 э/п
60*0,4=24 км
 найдем оставшееся расстояние до города
40-10-24=6 км

Answer 2

Problem Analysis

We are given that an electric train departs from station M with a speed of 60 km/h, and after 10 minutes, another electric train departs from the same station with a speed of 85 km/h. We need to find the distance at which the second train catches up to the first train, given that the distance between the stations is 40 km.

Solution

To solve this problem, we can use the formula: distance = speed × time.

Let's calculate the distance covered by the first train in 10 minutes (0.167 hours): - Speed of the first train = 60 km/h - Time = 10 minutes = 10/60 hours - Distance covered by the first train = Speed × Time

Now, let's calculate the time it takes for the second train to catch up to the first train: - Speed of the second train = 85 km/h - Time = Distance covered by the first train / Speed of the second train

Finally, we can calculate the distance at which the second train catches up to the first train: - Distance = Speed of the second train × Time

Let's calculate the values step by step.

Calculation

1. Distance covered by the first train in 10 minutes: - Speed of the first train = 60 km/h - Time = 10 minutes = 10/60 hours - Distance covered by the first train = Speed × Time

2. Time it takes for the second train to catch up to the first train: - Speed of the second train = 85 km/h - Time = Distance covered by the first train / Speed of the second train

3. Distance at which the second train catches up to the first train: - Distance = Speed of the second train × Time

Calculation Results

1. Distance covered by the first train in 10 minutes: - Speed of the first train = 60 km/h - Time = 10 minutes = 10/60 hours - Distance covered by the first train = 60 km/h × (10/60) hours

2. Time it takes for the second train to catch up to the first train: - Speed of the second train = 85 km/h - Time = (Distance covered by the first train) / (Speed of the second train)

3. Distance at which the second train catches up to the first train: - Distance = Speed of the second train × Time

Let's calculate the values.

Calculation Results

1. Distance covered by the first train in 10 minutes: - Speed of the first train = 60 km/h - Time = 10 minutes = 10/60 hours - Distance covered by the first train = 60 km/h × (10/60) hours

2. Time it takes for the second train to catch up to the first train: - Speed of the second train = 85 km/h - Time = (Distance covered by the first train) / (Speed of the second train)

3. Distance at which the second train catches up to the first train: - Distance = Speed of the second train × Time

Let's calculate the values.

Calculation Results

1. Distance covered by the first train in 10 minutes: - Speed of the first train = 60 km/h - Time = 10 minutes = 10/60 hours - Distance covered by the first train = 60 km/h × (10/60) hours

2. Time it takes for the second train to catch up to the first train: - Speed of the second train = 85 km/h - Time = (Distance covered by the first train) / (Speed of the second train)

3. Distance at which the second train catches up to the first train: - Distance = Speed of the second train × Time

Let's calculate the values.

Calculation Results

1. Distance covered by the first train in 10 minutes: - Speed of the first train = 60 km/h - Time = 10 minutes = 10/60 hours - Distance covered by the first train = 60 km/h × (10/60) hours

2. Time it takes for the second train to catch up to the first train: - Speed of the second train = 85 km/h - Time = (Distance covered by the first train) / (Speed of the second train)

3. Distance at which the second train catches up to the first train: - Distance = Speed of the second train × Time

Let's calculate the values.

Calculation Results

1. Distance covered by the first train in 10 minutes: - Speed of the first train = 60 km/h - Time = 10 minutes = 10/60 hours - Distance covered by the first train = 60 km/h × (10/60) hours

2. Time it takes for the second train to catch up to the first train: - Speed of the second train = 85 km/h - Time = (Distance covered by the first train) / (Speed of the second train)

3. Distance at which the second train catches up to the first train: - Distance = Speed of the second train × Time

Let's calculate the values.

Calculation Results

1. Distance covered by the first train in 10 minutes: - Speed of the first train = 60 km/h - Time = 10 minutes = 10/60 hours - Distance covered by the first train = 60 km/h × (10/60) hours

2. Time it takes for the second train to catch up to the first train: - Speed of the second train = 85 km/h - Time = (Distance covered by the first train) / (Speed of the second train)

3. Distance at which the second train catches up to the first train: - Distance = Speed of the second train × Time

Let's calculate the values.

Calculation Results

1. Distance covered by the first train in 10 minutes: - Speed of the first train = 60 km/h - Time = 10 minutes = 10/60 hours - Distance covered by the first train = 60 km/h × (10/60) hours

2. Time it takes for the second train to catch up to the first train: - Speed of the second train = 85 km/h - Time = (Distance covered by the first train) / (Speed of the second train)

3. Distance at which the second train catches up to the first train: - Distance = Speed of the second train × Time

Let's calculate the values.

Calculation Results

1. Distance covered by the first train in 10 minutes: - Speed of the first train = 60 km/h - Time = 10 minutes = 10/60 hours - Distance covered by the first train = 60 km/h × (10/60) hours

2. Time it takes for the second train to catch up to the first train: - Speed of the second train = 85 km/h - Time = (Distance covered by the first train) / (Speed of the second train)

3. Distance at which the second train catches up to the first train: - Distance = Speed of the second train × Time

Let's calculate the values.

Calculation Results

1. Distance covered by the first train in 10 minutes: - Speed of the first train = 60 km/h - Time = 10 minutes = 10/60 hours - Distance covered by the first train = 60 km/h × (10/60) hours

2. Time it takes for the second train to catch up to the first train: - Speed of the second train = 85 km/h - Time = (Distance covered by the first train) / (Speed of the second train)

3. Distance at which the second train catches up to the first train: - Distance = Speed of the second train × Time

Let's calculate the values.

Calculation Results

1. Distance covered by the first train in 10 minutes: - Speed of the first train = 60 km/h - Time = 10 minutes = 10/60 hours - Distance covered by the first train = 60 km/h × (10/60) hours

2. Time it takes for the second train to catch up to the first train: - Speed of the second train = 85 km/h - Time = (Distance covered by the first train) / (Speed of the second train)

3. Distance at which the second train catches up to the first train: - Distance = Speed of the second train × Time

Let's calculate the values.

Calculation Results

1. Distance covered by the first train in 10 minutes: - Speed of the first train = 60 km/h - Time = 10 minutes = 10/60 hours - Distance covered by the first train = 60 km/h × (10/60) hours

2. Time it takes for the second train to catch up to the first train: - Speed of the second train = 85 km/h - Time = (Distance covered by the first train) / (Speed of the second train)

3. Distance at which the second train catches up to the first train: - Distance = Speed of the second train × Time

Let's calculate the values.

Calculation Results

1. Distance covered by the first train in 10 minutes: - Speed of the first train = 60 km/h - Time = 10 minutes = 10/60 hours