Question

Автомобиль должен был проехать 1620км. После того, как он проехал 4/9 пути, его задержали на 2ч. Увеличив скорость на 5км/ч, автомобиль прибыл в пункт назначения вовремя. С какой скоростью ехал автомобиль после задержки?Желательно с таблицей

Answer 1

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Answer 2

Problem Analysis

We are given that a car was supposed to travel a distance of 1620 km. However, after traveling 4/9 of the distance, the car was delayed by 2 hours. To make up for the delay, the car increased its speed by 5 km/h and arrived at its destination on time. We need to find the speed of the car after the delay.

Solution

Let's break down the problem step by step:

1. Calculate the distance traveled by the car before the delay: - The car traveled 4/9 of the total distance, which is (4/9) * 1620 km. - Simplifying, we find that the car traveled 720 km before the delay.

2. Calculate the time taken by the car before the delay: - We know that speed = distance / time. - Rearranging the formula, we have time = distance / speed. - Let's assume the initial speed of the car before the delay is 'x' km/h. - Therefore, the time taken by the car before the delay is 720 km / x km/h.

3. Calculate the time taken by the car after the delay: - The car was delayed by 2 hours, so the total time taken by the car is the time taken before the delay plus the delay time, which is 720 km / x km/h + 2 hours.

4. Calculate the speed of the car after the delay: - To calculate the speed, we need to know the total distance traveled by the car after the delay. - The total distance traveled by the car is the remaining distance, which is 1620 km - 720 km, plus the distance covered at the increased speed. - The distance covered at the increased speed is the speed after the delay multiplied by the time taken after the delay. - Therefore, the total distance traveled by the car after the delay is (1620 km - 720 km) + (speed after delay * time taken after delay). - We know that the car arrived at its destination on time, so the time taken after the delay is the same as the time taken before the delay. - Substituting the values, the total distance traveled by the car after the delay is 900 km + (speed after delay * (720 km / x km/h + 2 hours)).

5. Set up an equation to solve for the speed after the delay: - The speed after the delay is x + 5 km/h (increased speed). - Setting up the equation, we have: (1620 km - 720 km) + (x + 5 km/h) * (720 km / x km/h + 2 hours) = 900 km + (x + 5 km/h) * (720 km / x km/h).

6. Solve the equation to find the speed after the delay: - Solving the equation will give us the value of x, which represents the speed of the car before the delay. - We can then calculate the speed after the delay by adding 5 km/h to x.

Let's summarize the steps in a table:

| Step | Calculation | |------|-----------------------------------------------------------------------------------------------------| | 1 | Distance traveled before the delay = (4/9) * 1620 km = 720 km | | 2 | Time taken before the delay = 720 km / x km/h | | 3 | Time taken after the delay = 720 km / x km/h + 2 hours | | 4 | Total distance traveled after the delay = 900 km + (x + 5 km/h) * (720 km / x km/h + 2 hours) | | 5 | Set up the equation: (1620 km - 720 km) + (x + 5 km/h) * (720 km / x km/h + 2 hours) = Total distance | | 6 | Solve the equation for x, then calculate the speed after the delay: x + 5 km/h |

Let's solve the equation and find the speed after the delay.