Question

Из двух сел по грунтовой дороге выехали одновременно навстречу друг другу 2 автомобиля. Первый за 2,4 часа проехал 9/70 всего расстояния между селами, а второй за 2 часа проехал 13/140 этого расстояния. С какой скоростью ехал первый автомобиль, если до места встречи второй проехал 351 км?

Answer 1

9/70:2,4=9/70*1/2,4=9/168=3/56 части дороги в час -скорость 1го
 13/140:2=13/140*1/2=13/280-части дороги в час -скорость 2го
3/56+13/280=15/280+13/280=28/280=1/10-части дороги в час -скорость сближения
351:3/56=351*56/3=117*56=6552-это время до встречи, но не в часах, а в км/часть дороги * час
6552*1/10=655,2км-весь путь(6552 км/часть пути*час *1/10части дороги/ час=655 км-это я как км получились из странных единиц)
655,2*3/56=35,1 км/ч-скорость 1го

Answer 2

Problem Analysis

We have two cars traveling towards each other on a dirt road. The first car takes 2.4 hours to travel a certain distance, while the second car takes 2 hours to travel a different fraction of that distance. We need to find the speed of the first car.

Solution

Let's assume the total distance between the two villages is D.

According to the problem, the first car travels 9/70 of the total distance in 2.4 hours, and the second car travels 13/140 of the total distance in 2 hours.

To find the speed of the first car, we can use the formula:

Speed = Distance / Time

Let's calculate the distance traveled by each car:

- Distance traveled by the first car = (9/70) * D - Distance traveled by the second car = (13/140) * D

Now, let's calculate the speed of the first car:

- Speed of the first car = Distance traveled by the first car / Time taken by the first car

We know that the time taken by the first car is 2.4 hours, so:

- Speed of the first car = (9/70) * D / 2.4

We are also given that the second car traveled a distance of 351 km before reaching the meeting point. Since the total distance between the two villages is D, the remaining distance traveled by the first car is D - 351.

We can set up the following equation:

(9/70) * (D - 351) / 2.4 = (13/140) * D / 2

Now, let's solve this equation to find the value of D:

(9/70) * (D - 351) / 2.4 = (13/140) * D / 2

Simplifying the equation:

(9/70) * (D - 351) * 2 = (13/140) * D * 2.4

Cross-multiplying:

(9/70) * (D - 351) * 2 * 140 = (13/140) * D * 2.4 * 70

Simplifying further:

(9/70) * (D - 351) * 280 = (13/140) * D * 168

Expanding:

(9/70) * (280D - 98280) = (13/140) * (168D)

Simplifying:

(9/70) * 280D - (9/70) * 98280 = (13/140) * 168D

Multiplying through by the denominators:

(9 * 280D) - (9 * 98280) = (13 * 168D) * (70)

Simplifying further:

2520D - 884520 = 23688D

Bringing like terms together:

2520D - 23688D = 884520

Simplifying:

-21168D = 884520

Dividing both sides by -21168:

D = 884520 / -21168

Calculating the value of D:

D ≈ -41.8

Since distance cannot be negative, we can conclude that there is an error in the problem statement or the calculations.

Please double-check the information provided and ensure that the values and fractions are accurate.