Question

Автомобиль ехал 4,3 часа со скоростью 80 км/ч и 3,2 часа со скоростью 75км/ч и еще 2,5 часа. С какой скоростью он ехал эти 2,5 часа, если средняя скорость автомобиля на всем пути равна 78,9 км/ч?

Answer 1

$\frac{(80+75+x)}{3}=78,9$
$80+75+x=78,9*3$
$80+75+x=236,7$
$x=236,7-80-75$
$x=81,7$ км/ч

Answer 2

Problem Analysis

The problem states that a car traveled for 4.3 hours at a speed of 80 km/h, then for 3.2 hours at a speed of 75 km/h, and finally for 2.5 hours at an unknown speed. The average speed of the car for the entire journey is given as 78.9 km/h. We need to find the speed of the car during the last 2.5 hours.

Solution

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

Let's calculate the distances traveled during each leg of the journey:

1. Distance traveled during the first leg: distance1 = speed1 * time1 = 80 km/h * 4.3 hours. 2. Distance traveled during the second leg: distance2 = speed2 * time2 = 75 km/h * 3.2 hours. 3. Total distance traveled: total_distance = distance1 + distance2.

Next, we can calculate the average speed of the car for the entire journey:

average_speed = total_distance / total_time.

We know that the total time is the sum of the times for all three legs of the journey:

total_time = time1 + time2 + time3.

We can rearrange the formula for average speed to solve for the total distance:

total_distance = average_speed * total_time.

Now, we can substitute the values we have into the formulas and solve for the total distance:

total_distance = 78.9 km/h * (4.3 hours + 3.2 hours + 2.5 hours).

Finally, we can find the speed during the last 2.5 hours by dividing the total distance by the time:

speed3 = total_distance / time3.

Let's calculate the values:

Calculation

1. Distance traveled during the first leg: distance1 = 80 km/h * 4.3 hours = 344 km. 2. Distance traveled during the second leg: distance2 = 75 km/h * 3.2 hours = 240 km. 3. Total distance traveled: total_distance = distance1 + distance2 = 344 km + 240 km = 584 km. 4. Total time: total_time = 4.3 hours + 3.2 hours + 2.5 hours = 10 hours. 5. Average speed: average_speed = total_distance / total_time = 584 km / 10 hours = 58.4 km/h. 6. Speed during the last 2.5 hours: speed3 = total_distance / time3 = 584 km / 2.5 hours.

Let's calculate the speed during the last 2.5 hours:

speed3 = 584 km / 2.5 hours = 233.6 km/h.

Answer

The car traveled at a speed of 233.6 km/h during the last 2.5 hours of the journey.