Question

Аул расположен между станцией и дачным поселком на расстоянии 4 км от станции. Из аула в сторону дачного поселка вышел пешеход со скоростью 75 м/мин. Через 0,5 ч со станции в том же направлении выехал велосипедист со скоростью 200 м/мин. Через сколько минут велосипедист догонит пешехода??? Решите задачу с помощью линейного уравнения.

Answer 1

75*30=225м прошёл пешеход за 30мин 225:200=1.1/8 мин догонит велосипедист пешехода

Answer 2

Problem Analysis

To solve this problem, we can use the linear equation \( s = vt \), where \( s \) is the distance, \( v \) is the speed, and \( t \) is the time. We'll use this equation to find the time it takes for the bicyclist to catch up to the pedestrian.

Solution

The pedestrian's speed is 75 m/min, and the distance to the dacha settlement is 4 km (4000 m). The bicyclist's speed is 200 m/min.

We can use the equation \( s = vt \) to find the time it takes for the bicyclist to catch up to the pedestrian. Let's denote \( t \) as the time it takes for the bicyclist to catch up to the pedestrian.

For the pedestrian: - \( s = 4000 \) m - \( v = 75 \) m/min

For the bicyclist: - \( v = 200 \) m/min

Using the equation \( s = vt \), we can solve for \( t \) for both the pedestrian and the bicyclist.

For the pedestrian: \[ 4000 = 75t \] \[ t = \frac{4000}{75} \] \[ t \approx 53.33 \] minutes

For the bicyclist: \[ 4000 = 200t \] \[ t = \frac{4000}{200} \] \[ t = 20 \] minutes

Answer

The bicyclist will catch up to the pedestrian in approximately 20 minutes.

I hope this helps! If you have further questions, feel free to ask.