Question

(5б) З міста А в місто В виїхав автобус. Через 20 хв. слідом за ним виїхав легковий автомобіль, який прибув в місто В на 20 хв. раніше за автобус. Знайти відстань між містами, якщо швидкість автобуса 60 км/год, а швидкість легкового автомобіля 80 км/год.

Answer 1

20 мин=1/3 ч
х - расстояние между А и В
х/60 - время движения автобуса от А до В
х/80 - время движения автомобиля от А до В
Автомобиль на 1/3 часа выехал позже и на 1/3 часа приехал раньше, значит он ехал на 1/3+1/3=2/3 часа меньше, чем автобус
х/60-х/80=2/3   (умножить на 240)
4х-3х=160
х=160 (км)
Ответ: расстояние между А и В 160 км

Answer 2

Problem Analysis

We are given that a bus traveled from city A to city B, and 20 minutes later, a car also traveled from city A to city B. The car arrived in city B 20 minutes earlier than the bus. We need to find the distance between the two cities given that the bus's speed is 60 km/h and the car's speed is 80 km/h.

Solution

Let's assume that the distance between city A and city B is d kilometers.

We can use the formula distance = speed × time to find the time it took for each vehicle to travel from city A to city B.

For the bus: - Speed = 60 km/h - Time = t hours (to be determined)

For the car: - Speed = 80 km/h - Time = t - 1/3 hours (20 minutes is equal to 1/3 of an hour)

Since the car arrived 20 minutes earlier than the bus, we subtract 1/3 from the time it took for the bus.

Now, we can set up the following equation based on the distances traveled by each vehicle:

60t = 80(t - 1/3)

Let's solve this equation to find the value of t.

Calculation

60t = 80(t - 1/3)

Expanding the equation:

60t = 80t - 80/3

Combining like terms:

80t - 60t = 80/3

Simplifying:

20t = 80/3

Dividing both sides by 20:

t = (80/3) / 20

Simplifying:

t = 4/3

The time it took for the bus to travel from city A to city B is 4/3 hours.

Now, we can calculate the distance between the two cities using the formula distance = speed × time.

For the bus: - Speed = 60 km/h - Time = 4/3 hours

For the car: - Speed = 80 km/h - Time = (4/3) - 1/3 = 1 hour

Let's calculate the distances:

Distance = Speed × Time

For the bus: Distance = 60 × (4/3) = 80 kilometers

For the car: Distance = 80 × 1 = 80 kilometers

Therefore, the distance between city A and city B is 80 kilometers.

Answer

The distance between city A and city B is 80 kilometers.