Question

Легковий автомобіль за 5 год проїхав таку саму відстань як грузовик за 8 год.Знайдіть швидкість грузового автомобіля , якщо вона на 45км/год меньше за швидкість легкового. Порівнйте швидкості автомобілів ​

Answer 1

Відповідь:

скорость грузового х км/час

скорость легкового (х+30) км/час

грузовой за 4 часа прошел 4х км

легковой за 3 часа 3(х+30) км

и эти пути равны

4x = 3(x+30)

4x = 3x +90

x = 90 (км/час)

тогда скорость легкового 90+30 = 120 км/час

Пояснення:

Answer 2

To find the speed of the truck, we can use the formula: speed = distance / time. Let's assume the distance traveled by both the car and the truck is "d" kilometers.

Given that the car traveled the same distance in 5 hours and the truck traveled the same distance in 8 hours, we can set up the following equations:

Car: speed_car = d / 5 Truck: speed_truck = d / 8

We also know that the speed of the truck is 45 km/h less than the speed of the car. Therefore, we can write another equation:

speed_truck = speed_car - 45

To solve this system of equations, we can substitute the value of speed_car from the first equation into the second equation:

d / 8 = (d / 5) - 45

Now, let's solve this equation step by step:

Step 1:

Multiply both sides of the equation by 40 (the least common multiple of 8 and 5) to eliminate the denominators:

40 * (d / 8) = 40 * ((d / 5) - 45)

Step 2:

Simplify both sides of the equation:

5d = 8d - 1800

Step 3:

Subtract 8d from both sides of the equation:

5d - 8d = -1800

Step 4:

Combine like terms:

-3d = -1800

Step 5:

Divide both sides of the equation by -3:

d = -1800 / -3

Step 6:

Simplify:

d = 600

Now that we have found the value of "d" (the distance traveled by both the car and the truck), we can substitute it back into one of the original equations to find the speed of the truck.

Using the equation for the car's speed:

speed_car = d / 5 speed_car = 600 / 5 speed_car = 120 km/h

Since the speed of the truck is 45 km/h less than the speed of the car, we can calculate the speed of the truck:

speed_truck = speed_car - 45 speed_truck = 120 - 45 speed_truck = 75 km/h

Therefore, the speed of the truck is 75 km/h, while the speed of the car is 120 km/h.

Please note that the negative sign in the distance value (-1800) was ignored since distance cannot be negative in this context.