Question

Из пункта А в пункт В одновременно выехали две легковые машины. скорость одной из них равна 75 км/ч,что на 15 км/ч больше скорости второй .найдите расстояние между пунктами А и В ,если в пункт В первая машина приехала на 1 ч 12мин раньше другой.

Answer 1

Скорость первой 75км/ч,время хч
Скорость второй 75-15=60км/ч,время х+1 1/5ч
75*х=60*(х+6/5)
75х-60х=72
15х=72
х=72:15
х=4,8
75*4,8=360км расстояние

Answer 2

Problem Analysis

We are given that two cars simultaneously left point A and traveled to point B. The speed of one car is 75 km/h, which is 15 km/h faster than the speed of the other car. The first car arrived at point B 1 hour and 12 minutes earlier than the second car. We need to find the distance between points A and B.

Solution

Let's assume the speed of the second car is x km/h. Since the speed of the first car is 15 km/h faster, its speed is x + 15 km/h.

We know that the time taken by the second car to travel from A to B is 1 hour and 12 minutes longer than the time taken by the first car. Let's convert 1 hour and 12 minutes to hours: 1 hour + 12 minutes/60 = 1.2 hours.

We can use the formula distance = speed × time to find the distance between points A and B.

For the first car: - Speed = x + 15 km/h - Time = t hours (unknown)

For the second car: - Speed = x km/h - Time = t + 1.2 hours

The distance traveled by both cars is the same, so we can set up the equation:

distance of first car = distance of second car

Using the formula distance = speed × time, we can write:

(x + 15) × t = x × (t + 1.2)

Simplifying the equation:

xt + 15t = xt + 1.2x + 1.2

Subtracting xt from both sides:

15t = 1.2x + 1.2

Now we have an equation with two variables, t and x. We need another equation to solve for both variables.

We know that the speed of the second car is 75 km/h, so we can write another equation:

x = 75 - 15

Simplifying:

x = 60

Now we can substitute this value of x into the first equation:

15t = 1.2(60) + 1.2

Simplifying:

15t = 72 + 1.2

15t = 73.2

Dividing both sides by 15:

t = 73.2 / 15

t = 4.88

Now we have the value of t. We can substitute it back into the equation x = 60 to find the speed of the second car.

x = 60 km/h

The distance between points A and B can be found using the formula distance = speed × time. We can use the speed of the second car and the time it took to travel from A to B.

distance = 60 km/h × 4.88 hours

Calculating:

distance = 292.8 km

Therefore, the distance between points A and B is 292.8 km.

Answer

The distance between points A and B is 292.8 km.