Question

Составить уравнения. Группа туристов 1 ч ехала на автобусе, а затем 6 ч шла пешком со скоростью на 18 км/ч меньше, чем скорость автобуса. Всего группа преодолела 67 км. Найдите скорость автобуса и туристов в пешем походе.

Answer 1

1) Выберем за Х км/ч скорость автобуса, тогда ( Х-18 ) км/ч скорость пешком;
1*Х+6*(Х-18)=67
Х+6Х-108=67
7Х=67+108
7Х=175
Х=175/7
Х=25 км/ч ( скорость автобуса)
2) 25км/ч-18км/ч=7км/ч ( скорость пешком).

Answer 2

Problem Analysis

We are given that a group of tourists traveled on a bus for 1 hour and then walked for 6 hours at a speed that is 18 km/h less than the speed of the bus. The total distance covered by the group is 67 km. We need to find the speed of the bus and the speed of the tourists while walking.

Solution

Let's assume the speed of the bus is x km/h. Since the speed of the tourists while walking is 18 km/h less than the speed of the bus, their speed is (x - 18) km/h.

We can use the formula distance = speed × time to calculate the distances covered by the bus and the tourists while walking.

The distance covered by the bus in 1 hour is x km.

The distance covered by the tourists while walking in 6 hours is (x - 18) × 6 km.

According to the problem, the total distance covered by the group is 67 km. Therefore, we can write the equation:

x + (x - 18) × 6 = 67

Let's solve this equation to find the values of x and (x - 18).

Solving the Equation

Expanding the equation, we get:

x + 6x - 108 = 67

Combining like terms, we get:

7x - 108 = 67

Adding 108 to both sides of the equation, we get:

7x = 175

Dividing both sides of the equation by 7, we get:

x = 25

Therefore, the speed of the bus is 25 km/h.

Substituting this value back into the equation, we can find the speed of the tourists while walking:

(x - 18) = (25 - 18) = 7 km/h

Therefore, the speed of the tourists while walking is 7 km/h.

Answer

The speed of the bus is 25 km/h and the speed of the tourists while walking is 7 km/h.

Verification

Let's verify our answer by substituting the values back into the original equation:

25 + (25 - 18) × 6 = 67

Simplifying the equation, we get:

25 + 7 × 6 = 67

25 + 42 = 67

67 = 67

The equation is true, which means our answer is correct.

Conclusion

The speed of the bus is 25 km/h and the speed of the tourists while walking is 7 km/h.