Question

От города до посёлка мотоциклист доехал за 3 часа. Если бы он увеличил скорость на 25 км/ч, то проехал бы это расстояние за 2 часа. Чему равно расстояние от город до посёлка? Решите задачу обозначив буквой искомое расстояние

Answer 1

S - расстояние
V * 3 час = S
(V + 25 км/час) * 2 час = S
V * 3 час = (V + 25 км/час) * 2 час
3V = 2V + 50
3V - 2V = 50
V = 50 км/час
S = 50 км/час * 3 час
S = 150 км

Ответ: расстояние равно 150 км

Answer 2

Problem Analysis

We are given that a motorcyclist traveled from a city to a village in 3 hours. If the motorcyclist had increased their speed by 25 km/h, they would have covered the same distance in 2 hours. We need to find the distance from the city to the village.

Let's denote the distance from the city to the village as d.

Solution

To solve this problem, we can set up a system of equations based on the given information.

Let's assume the initial speed of the motorcyclist is v km/h. According to the problem, if the motorcyclist had increased their speed by 25 km/h, they would have covered the distance in 2 hours. Therefore, the speed in this case would be v + 25 km/h.

Using the formula distance = speed × time, we can set up the following equations:

Equation 1: d = v × 3 (since the motorcyclist covered the distance in 3 hours)

Equation 2: d = (v + 25) × 2 (since the motorcyclist would have covered the distance in 2 hours if their speed was increased by 25 km/h)

Now, let's solve this system of equations to find the value of d.

Solving the System of Equations

We can start by simplifying Equation 2:

d = (v + 25) × 2

Expanding the equation:

d = 2v + 50

Now, we can substitute Equation 1 into this simplified version of Equation 2:

v × 3 = 2v + 50

Simplifying further:

3v = 2v + 50

Subtracting 2v from both sides:

v = 50

Now that we have the value of v, we can substitute it back into Equation 1 to find the value of d:

d = v × 3 = 50 × 3 = 150

Therefore, the distance from the city to the village is 150 kilometers.

Answer

The distance from the city to the village is 150 kilometers.

Verification

Let's verify our answer using the given information.

According to the problem, if the motorcyclist had increased their speed by 25 km/h, they would have covered the distance in 2 hours. Let's calculate the distance using this information:

Speed = v + 25 = 50 + 25 = 75 km/h

Distance = Speed × Time = 75 × 2 = 150 km

The calculated distance matches our answer, so our solution is correct.

Conclusion

The distance from the city to the village is 150 kilometers.