Question

Саша вышел на лыжную тренировку в 8 ч утра. Через 15 мин вслед за ним выбежал пёс Шарик. Через сколько минут Шарик догонит Сашу, если он бежит со скоростью 310 м/мин, а Саша идет со скоростью 260 м/мин? Какое время будет на часах в тот момент, когда Шарик догонит Сашу?

Answer 1

260*15=3900 м. проехал Саша за 15 мин.
x мин. - время, за которое шарик догонит Сашу
3900+260x=310x
50x=3900
x=78 мин.=1ч 18мин 
8ч. 15мин.+1ч. 18мин.=9ч. 33мин.

Answer 2

Problem Analysis

To solve this problem, we need to determine how long it will take for the dog, Sharik, to catch up to Sasha. We are given that Sasha is skiing at a speed of 260 m/min and Sharik is running at a speed of 310 m/min. We also know that Sharik starts running 15 minutes after Sasha.

Calculating the Time

To calculate the time it takes for Sharik to catch up to Sasha, we can use the formula:

Time = Distance / Speed

Since both Sasha and Sharik are moving at a constant speed, we can assume that the distance between them remains constant. Therefore, we can set up the following equation:

Distance = Speed of Sasha * Time

We can also calculate the distance covered by Sharik using the same formula:

Distance = Speed of Sharik * (Time - 15 minutes)

Setting these two equations equal to each other, we can solve for the time it takes for Sharik to catch up to Sasha.

Solution

Let's calculate the time it takes for Sharik to catch up to Sasha.

Step 1: Calculate the distance covered by Sasha in 15 minutes: Distance covered by Sasha = Speed of Sasha * Time Distance covered by Sasha = 260 m/min * 15 min Distance covered by Sasha = 3900 m

Step 2: Set up the equation for the distance covered by Sharik: Distance covered by Sharik = Speed of Sharik * (Time - 15 minutes)

Step 3: Set the distances covered by Sasha and Sharik equal to each other and solve for Time: 260 m/min * Time = 310 m/min * (Time - 15 min)

Step 4: Solve the equation for Time: 260 * Time = 310 * (Time - 15) 260 * Time = 310 * Time - 310 * 15 260 * Time - 310 * Time = -310 * 15 -50 * Time = -4650 Time = -4650 / -50 Time = 93 minutes

Therefore, it will take 93 minutes for Sharik to catch up to Sasha.

Calculating the Time on the Clock

To determine the time on the clock when Sharik catches up to Sasha, we need to add the time it takes for Sharik to catch up to Sasha (93 minutes) to the initial time when Sasha started his ski training (8:00 AM).

Step 1: Convert 93 minutes to hours: 93 minutes = 93 / 60 hours 93 minutes = 1.55 hours

Step 2: Add the hours to the initial time: 8:00 AM + 1.55 hours = 9:33 AM

Therefore, the time on the clock when Sharik catches up to Sasha will be approximately 9:33 AM.