Question

Из двух городов,расстояние между которыми 168км, одновременно навстречу друг другу выехали автобус и легковой автомобиль. Скорость автомобиля на 12км /ч больше скорости автобуса.Они встретились через 1 ч 30 мин. Найдите скорость автобуса.

Answer 1

X -  скорость автобуса 
(х + 12) - скорость автомобиля
Из условия задачи имеем : 168 /( х + (х +12) = 1,5
168 / ( х + х +12) = 1,5
112 / (2х + 12) = 1
112 = 2х + 12
112 - 12 = 2х
2х = 100
х = 100 / 2
х = 50 км/ч - скорость автобуса

Answer 2

Problem Analysis

We are given that two vehicles, a bus and a car, start simultaneously from two cities that are 168 km apart. The car's speed is 12 km/h faster than the bus's speed. After 1 hour and 30 minutes, the two vehicles meet each other. We need to find the speed of the bus.

Solution

Let's assume the speed of the bus is x km/h. Since the car's speed is 12 km/h faster, the speed of the car is (x + 12) km/h.

We know that the distance traveled by both vehicles is the same, which is 168 km. We can use the formula distance = speed × time to set up two equations:

For the bus: x km/h × (1.5 hours) = 168 km

For the car: (x + 12) km/h × (1.5 hours) = 168 km

Simplifying these equations, we get:

1.5x = 168 1.5(x + 12) = 168

Now, let's solve these equations to find the value of x.

Calculation

Equation 1: 1.5x = 168 Divide both sides by 1.5: x = 168 / 1.5 x = 112

Equation 2: 1.5(x + 12) = 168 Distribute 1.5: 1.5x + 18 = 168 Subtract 18 from both sides: 1.5x = 150 Divide both sides by 1.5: x = 150 / 1.5 x = 100

Answer

The speed of the bus is 100 km/h.

Explanation

The bus and the car meet each other after 1 hour and 30 minutes, which is 1.5 hours. The bus's speed is 100 km/h, so in 1.5 hours, it travels 100 km/h × 1.5 hours = 150 km. The car's speed is 12 km/h faster, so its speed is 112 km/h. In 1.5 hours, the car travels 112 km/h × 1.5 hours = 168 km. Since the distance between the two cities is 168 km, the bus and the car meet each other at that point.

Verification

Let's verify our solution using the given information.

The bus's speed is 100 km/h, and the car's speed is 112 km/h. After 1.5 hours, the bus travels 100 km/h × 1.5 hours = 150 km, and the car travels 112 km/h × 1.5 hours = 168 km. The total distance traveled by both vehicles is 150 km + 168 km = 318 km. Since the distance between the two cities is 168 km, the sum of the distances traveled by the bus and the car is equal to the distance between the two cities. Therefore, our solution is verified.

Conclusion

The speed of the bus is 100 km/h.