Question

девочка прошла первую половину пути за время равное t1=15 минут оставшуюся часть она двигалась со скоростью 3км/ч найдите полный пусть пройденный девочкой если средняя скорость за все время движения 4 км/ч

Answer 1

Ответ:

3 км

Объяснение:

См.фото

Answer 2

Problem Analysis

We are given that a girl has completed the first half of her journey in 15 minutes, and for the remaining part, she moved at a speed of 3 km/h. We need to find the total distance covered by the girl if her average speed for the entire journey is 4 km/h.

Solution

To solve this problem, we can break it down into two parts: the distance covered in the first half of the journey and the distance covered in the second half of the journey.

Let's assume the total distance covered by the girl is D.

Distance Covered in the First Half

We are given that the girl completed the first half of her journey in 15 minutes. Since the average speed is 4 km/h, we can calculate the distance covered in the first half using the formula:

Distance = Speed × Time

The speed is given as 4 km/h, and the time is given as 15 minutes. However, we need to convert the time to hours to match the speed unit. There are 60 minutes in an hour, so 15 minutes is equal to 15/60 = 0.25 hours.

Substituting the values into the formula, we get:

Distance in the First Half = 4 km/h × 0.25 h

Simplifying the expression, we find:

Distance in the First Half = 1 km

Distance Covered in the Second Half

We are given that the girl moved at a speed of 3 km/h for the remaining part of the journey. To find the distance covered in the second half, we can again use the formula:

Distance = Speed × Time

The speed is given as 3 km/h, and the time can be calculated by subtracting the time taken in the first half from the total time. The total time is not given, but we can calculate it using the average speed and the total distance.

The average speed is given as 4 km/h, and the total distance is D. We can use the formula:

Average Speed = Total Distance / Total Time

Rearranging the formula, we find:

Total Time = Total Distance / Average Speed

Substituting the values, we get:

Total Time = D / 4 km/h

Now, the time taken in the first half is given as 15 minutes, which is equal to 0.25 hours. So, the time taken in the second half can be calculated as:

Time in the Second Half = Total Time - Time in the First Half

Substituting the values, we get:

Time in the Second Half = (D / 4) - 0.25 hours

Now, we can calculate the distance covered in the second half using the formula:

Distance in the Second Half = Speed × Time

The speed is given as 3 km/h, and the time is calculated as (D / 4) - 0.25 hours.

Substituting the values, we get:

Distance in the Second Half = 3 km/h × [(D / 4) - 0.25]

Simplifying the expression, we find:

Distance in the Second Half = (3/4)D - 0.75 km

Total Distance Covered

The total distance covered by the girl is the sum of the distances covered in the first and second halves. So, we can add the two distances:

Total Distance = Distance in the First Half + Distance in the Second Half

Substituting the values, we get:

D = 1 km + (3/4)D - 0.75 km

Simplifying the expression, we find:

(1/4)D = 0.75 km

Multiplying both sides by 4, we get:

D = 3 km

Therefore, the total distance covered by the girl is 3 km.

Answer

The total distance covered by the girl is 3 km.

Verification

Let's verify the answer using the given information.

We are given that the girl completed the first half of her journey in 15 minutes, which is equal to 0.25 hours. The distance covered in the first half is 1 km.

For the remaining part of the journey, the girl moved at a speed of 3 km/h. The time taken in the second half can be calculated as:

Time in the Second Half = (Total Distance / Average Speed) - Time in the First Half

Substituting the values, we get:

Time in the Second Half = (3 km / 4 km/h) - 0.25 hours = 0.75 hours

The distance covered in the second half can be calculated using the formula:

Distance in the Second Half = Speed × Time

Substituting the values, we get:

Distance in the Second Half = 3 km/h × 0.75 hours = 2.25 km

The total distance covered is the sum of the distances covered in the first and second halves:

Total Distance = Distance in the First Half + Distance in the Second Half = 1 km + 2.25 km = 3.25 km

Since the average speed for the entire journey is 4 km/h, the total time taken can be calculated as:

Total Time = Total Distance / Average Speed = 3.25 km / 4 km/h = 0.8125 hours

Converting the total time to minutes, we get:

Total Time = 0.8125 hours × 60 minutes/hour = 48.75 minutes

Therefore, the total distance covered by the girl is indeed 3 km, which is consistent with our calculations.

Conclusion

The total distance covered by the girl is 3 km.