Question

мотоциклист может проехать расстояние между пунктами за 2 часа, а велосипедист-за 6 часов. однажды они одновременно отправились на встречу друг к другу. расстояние между пунктами 60 км. сколько километров проехал каждый

Answer 1

1)60:2=30 км/час-скорость мотоциклиста
2)60:6=10км/час-скорость велосипедиста
3)30+10=40(км/час)-суммарная скорость
4) 60:40=1,5(час)-время движения обоих
5)30*1,5=45(км)-проехал мотоциклист
6)10*1,5=15(км)-проехал велосипедист

Answer 2

#### Problem Analysis We have a scenario where a motorcyclist and a cyclist are traveling towards each other from two different points. The motorcyclist can cover the distance between the points in 2 hours, while the cyclist takes 6 hours. The distance between the points is 60 km. We need to determine how many kilometers each of them traveled. #### Solution Let's assume that the motorcyclist traveled **x** kilometers and the cyclist traveled **y** kilometers. Since they started at the same time and met each other, the sum of their distances should be equal to the total distance between the points. We can set up the following equation based on the given information: **x + y = 60** (equation 1) We also know that the motorcyclist can cover the distance in 2 hours, and the cyclist takes 6 hours. We can use the formula **speed = distance / time** to calculate their speeds. Let's assume the speed of the motorcyclist is **v1** km/h, and the speed of the cyclist is **v2** km/h. Based on the given information, we can set up the following equations: **x = v1 * 2** (equation 2) **y = v2 * 6** (equation 3) To solve the problem, we need to find the values of **x** and **y**. #### Solution Steps 1. Solve equation 2 for **v1**: **v1 = x / 2** 2. Solve equation 3 for **v2**: **v2 = y / 6** 3. Substitute the values of **v1** and **v2** into equation 1: **x + y = 60** **(x / 2) + (y / 6) = 60** 4. Multiply equation 1 by 6 to eliminate fractions: **6x + y = 360** (equation 4) 5. Substitute the value of **v1** from step 1 into equation 4: **6(x / 2) + y = 360** **3x + y = 360** (equation 5) 6. Solve equations 4 and 5 simultaneously to find the values of **x** and **y**. Let's solve the equations to find the values of **x** and **y**. #### Solution To solve the equations, we'll use the substitution method. From equation 5, we have **3x + y = 360**. Let's solve equation 5 for **y**: **y = 360 - 3x** (equation 6) Substitute equation 6 into equation 1: **x + (360 - 3x) = 60** **-2x = -300** **x = 150** Substitute the value of **x** into equation 6 to find **y**: **y = 360 - 3(150)** **y = 360 - 450** **y = -90** Since distance cannot be negative, we can conclude that there is no valid solution to this problem. #### Conclusion Based on the given information, it is not possible for the motorcyclist and cyclist to meet each other while traveling towards each other from two different points. The problem does not have a valid solution. Please let me know if there's anything else I can help you with!