Question

Расстояние между городами А и В равно 400 км. Из А в В выехала грузовая машина, а через 2 ч вслед за ней выехала легковая машина, скорость которой в 1,5 раза больше скорости грузовой. Найдите скорость грузовой машины, если известно, что она прибыла в В на 1 ч 20 мин позже легковой.

Answer 1

Problem Analysis

We are given that the distance between cities A and B is 400 km. A truck leaves city A, and 2 hours later, a car leaves city A at a speed 1.5 times faster than the truck. We need to find the speed of the truck if it arrives in city B 1 hour and 20 minutes later than the car.

Solution

Let's assume the speed of the truck is x km/h. Since the car is 1.5 times faster, its speed is 1.5x km/h.

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

The time taken by the truck is given by: time taken by truck = distance / speed of truck = 400 / x (in hours).

The time taken by the car is given by: time taken by car = distance / speed of car = 400 / (1.5x) (in hours).

We are given that the truck arrives in city B 1 hour and 20 minutes later than the car. Converting 1 hour and 20 minutes to hours, we get: 1 hour and 20 minutes = 1 + 20/60 = 1.33 hours.

According to the given information, the time taken by the truck is 1.33 hours more than the time taken by the car. So we can set up the following equation:

time taken by truck = time taken by car + 1.33.

Substituting the expressions for the times taken by the truck and the car, we get:

400 / x = 400 / (1.5x) + 1.33.

To solve this equation, we can multiply both sides by x to eliminate the denominators:

400 = 400 / 1.5 + 1.33x.

Simplifying the equation, we have:

400 = (400 / 1.5) + 1.33x.

Now we can solve for x to find the speed of the truck.

Calculation

Let's calculate the speed of the truck using the equation derived above.

400 = (400 / 1.5) + 1.33x.

Multiplying both sides by 1.5 to eliminate the fraction, we get:

600 = 400 + 1.33x.

Subtracting 400 from both sides, we have:

200 = 1.33x.

Dividing both sides by 1.33, we get:

x = 200 / 1.33 ≈ 150.38.

Therefore, the speed of the truck is approximately 150.38 km/h.

Answer

The speed of the truck is approximately 150.38 km/h.

Note: The answer is rounded to two decimal places.