Question

Из двух городов A и B, расстояние между которыми равно 126 км, одновременно выехали две автомашины. Скорость первой машины равна 85 км/ч, а скорость второй машины 43 км/ч. На каком расстоянии от города B обе машины встретятся и через какое время? Ответ: обе машины встретятся на расстоянии ___ км от города B, и это случится через ___ часа.

Answer 1

Если двигаются в одном направлении
85-43=42км/ч скорость сближения
126:42=3ч
43*3=129км
Ответ: обе машины встретятся на расстоянии 129 км от города B, и это случится через 3 часа.

Answer 2

Problem Analysis

We are given two cities, A and B, with a distance of 126 km between them. Two cars start simultaneously from these cities. The first car has a speed of 85 km/h, and the second car has a speed of 43 km/h. We need to determine at what distance from city B the two cars will meet and how much time it will take for them to meet.

Solution

To solve this problem, we can use the formula: distance = speed × time.

Let's assume that the two cars meet at a distance of x km from city B.

The time taken by the first car to reach the meeting point can be calculated as time1 = x / speed1, where speed1 is the speed of the first car.

Similarly, the time taken by the second car to reach the meeting point can be calculated as time2 = (126 - x) / speed2, where speed2 is the speed of the second car.

Since both cars start simultaneously, the time taken by both cars to reach the meeting point will be the same. Therefore, we can equate the two time expressions:

x / speed1 = (126 - x) / speed2

We can solve this equation to find the value of x.

Let's calculate the value of x and the time taken for the cars to meet.

Calculation

Given: - Distance between cities A and B = 126 km - Speed of the first car = 85 km/h - Speed of the second car = 43 km/h

Using the equation x / speed1 = (126 - x) / speed2, we can solve for x.

x / 85 = (126 - x) / 43

Cross-multiplying the equation:

43x = 85(126 - x)

Expanding and simplifying:

43x = 10710 - 85x

43x + 85x = 10710

128x = 10710

x = 10710 / 128

x ≈ 83.59

Therefore, the two cars will meet at a distance of approximately 83.59 km from city B.

To calculate the time taken for the cars to meet, we can substitute the value of x into either of the time expressions.

Using the time expression for the first car:

time1 = x / speed1

time1 = 83.59 / 85

time1 ≈ 0.983

Therefore, the two cars will meet approximately 0.983 hours (or 59 minutes) after they start.

Answer

The two cars will meet at a distance of approximately 83.59 km from city B, and this will happen approximately 0.983 hours (or 59 minutes) after they start.