Question

Дима шел вдоль реки к остановке автобуса. Не дойдя до остановки 3 км, он решил искупаться и потратил на это 15 минут. Чтобы успеть к автобусу вовремя, онувеличил скорость на 2 км/ч. С какой скоростью первоначально шел Дима?

Answer 1

Пусть первоначальная скорость  х км/ч, тогда увеличенная (х+2) км/ч. Время Дима мог наверстать на оставшихся 3 км - это 15 мин. = 1/4 часа. Уравнение

(3/x) - (3/(x+2)) = 1/4. После упрощения:  x^2 +2x -24 =0, Теорема Виета:

x = -6 - не подходит по смыслу задачи;  х = 4 - это и есть первоначальная скорость Димы. 

Answer 2

Calculation of Dima's Initial Walking Speed

To determine Dima's initial walking speed, we need to consider the distance he walked and the time it took him to swim.

Dima walked 3 km but did not reach the bus stop. He then spent 15 minutes swimming before continuing his journey. To make up for the time spent swimming, he increased his speed by 2 km/h.

Let's calculate Dima's initial walking speed step by step:

1. Convert the swimming time from minutes to hours: - Dima spent 15 minutes swimming, which is equivalent to 15/60 = 0.25 hours.

2. Calculate the distance Dima covered while swimming: - Dima's swimming speed is not given, so we cannot determine the distance he covered while swimming. Therefore, we will assume that the swimming distance is negligible compared to the walking distance.

3. Calculate the time it took Dima to walk the remaining distance after swimming: - Dima walked a total distance of 3 km but did not reach the bus stop. Therefore, he walked a distance of 3 km - 0 km (swimming distance) = 3 km. - Dima spent 15 minutes swimming, which is equivalent to 0.25 hours. - Let's assume Dima's initial walking speed is x km/h. - The time it took Dima to walk the remaining distance is given by the equation: time = distance / speed. - Therefore, 3 km / x km/h = 3 / x hours.

4. Calculate the time it took Dima to walk the remaining distance after increasing his speed: - After swimming, Dima increased his speed by 2 km/h. Therefore, his new walking speed is x + 2 km/h. - The time it took Dima to walk the remaining distance at the increased speed is given by the equation: time = distance / speed. - Therefore, 3 km / (x + 2) km/h = 3 / (x + 2) hours.

5. Set up an equation to solve for x: - The time it took Dima to walk the remaining distance before and after increasing his speed should be the same. - Therefore, we can set up the equation: 3 / x = 3 / (x + 2).

6. Solve the equation for x: - Cross-multiply the equation: 3 * (x + 2) = 3 * x. - Simplify the equation: 3x + 6 = 3x. - Subtract 3x from both sides: 6 = 0. - This equation has no solution, which means there is no value of x that satisfies the equation.

Based on the given information, it is not possible to determine Dima's initial walking speed.