Question

6 класс задача помогите пожалуйста! Велосипедист ехал по шоссе со скоростью 16 км/ч, а оставшейся путь по просёлочной дороге со скоростью 8 км/ч. Весь путь составил 64 км. Сколько минут велосипедист затратил на путь по шоссе, если по просёлочной дороге он ехал на 30 минут дольше, чем по шоссе?

Answer 1

30 минут = 0,5 часа

Пусть Х часов велосипедист ехал по шоссе, тогда:
х+0,5 часов - по проселочной дороге
16х км - проехал по шоссе
8*(х+0,5) км - проехал по проселочной дороге
Весь путь 64 км
Составим и решим уравнение:
$16x+8*(x+0.5)=64 \\ 16x+8x+4=64 \\ 24x=64-4 \\ 24x=60 \\ x=60:24$
$x=2,5$ часа затратил на путь по шоссе

Если нужен ответ в минутах, то 2,5 часа = 2*60 +30 = 150 минут

Проверка:
по проселочной дороге ехал на 0,5 часа дольше, чем по шоссе:
2,5 + 0,5 = 3 часа - по проселочной дороге
Весь путь:
2,5 * 16 + 3 * 8 = 40 + 24 = 64 км
Верно.

Answer 2

Problem Analysis

We are given that a cyclist traveled a certain distance on a highway at a speed of 16 km/h and the remaining distance on a dirt road at a speed of 8 km/h. The total distance traveled was 64 km. We need to find out how many minutes the cyclist spent on the highway if they spent 30 minutes longer on the dirt road than on the highway.

Solution

Let's assume that the cyclist spent x minutes on the highway. Since the speed on the highway is 16 km/h, the distance traveled on the highway can be calculated as 16 * (x/60) km.

The remaining distance on the dirt road can be calculated as 64 - 16 * (x/60) km.

We are given that the cyclist spent 30 minutes longer on the dirt road than on the highway. So, the time spent on the dirt road can be calculated as x + 30 minutes.

Since the speed on the dirt road is 8 km/h, the distance traveled on the dirt road can be calculated as 8 * ((x + 30)/60) km.

The sum of the distances traveled on the highway and the dirt road should be equal to the total distance of 64 km.

Let's set up the equation and solve for x:

16 * (x/60) + 8 * ((x + 30)/60) = 64

Calculation

To solve the equation, we can multiply both sides by 60 to eliminate the denominators:

16x + 8(x + 30) = 64 * 60

Simplifying the equation:

16x + 8x + 240 = 3840

Combining like terms:

24x + 240 = 3840

Subtracting 240 from both sides:

24x = 3600

Dividing both sides by 24:

x = 150

Therefore, the cyclist spent 150 minutes on the highway.

Answer

The cyclist spent 150 minutes on the highway.

Note: The above solution is based on the information provided in the problem statement.