Question

Канат проехал расстояние межу городами за 3 дня. в первый день он проехал 1/5 всего пути и еще 60 км, во второй 1/4 всего пути и еще 20 км,третий день 23/8 всего пути и оставшиеся 25 км. Найти расстояние между городами.

Answer 1

$\frac15+\frac14+\frac{23}{80}=\frac{16+20+23}{80}=\frac{59}{80}\\1-\frac{59}{80}=\frac{21}{80}\\60+20+25 = 105\\105:\frac{21}{80}=105\cdot\frac{80}{21}=5\cdot80=400$

Answer 2

Problem Analysis

We are given that a rope traveled a distance between two cities in 3 days. On the first day, it traveled 1/5 of the total distance plus an additional 60 km. On the second day, it traveled 1/4 of the total distance plus an additional 20 km. On the third day, it traveled 23/8 of the total distance plus the remaining 25 km. We need to find the total distance between the cities.

Solution

Let's assume the total distance between the cities is D km.

On the first day, the rope traveled 1/5 of the total distance plus an additional 60 km. This can be expressed as:

1/5 * D + 60 km

On the second day, the rope traveled 1/4 of the total distance plus an additional 20 km. This can be expressed as:

1/4 * D + 20 km

On the third day, the rope traveled 23/8 of the total distance plus the remaining 25 km. This can be expressed as:

23/8 * D + 25 km

According to the given information, the sum of these distances is equal to the total distance between the cities:

1/5 * D + 60 km + 1/4 * D + 20 km + 23/8 * D + 25 km = D

Simplifying the equation:

(1/5 + 1/4 + 23/8) * D + (60 + 20 + 25) km = D

(8/40 + 10/40 + 115/40) * D + 105 km = D

(133/40) * D + 105 km = D

Multiplying both sides by 40 to eliminate the fraction:

133 * D + 4200 km = 40 * D

133 * D - 40 * D = -4200 km

93 * D = -4200 km

D = -4200 km / 93

D ≈ -45.16 km

Since distance cannot be negative, it seems there might be an error in the given information or the calculations. Please double-check the values provided.

If you have any further questions, please let me know.