Question

Вася и Коля шли а гости к Саше . Коля шёл половину пути со скоростью 4 км/час, а другую половину со скоростью 5 км/ч , а Вася половину времени со скоростью 4 км/ч , а вторую половину со скоростью 5 км/ч .Из дома они вышли одновременно .Кто из мальчиков придёт первый ?

Answer 1

Problem Analysis

Vasya and Kolya are walking to Sasha's house. Kolya walks half the distance at a speed of 4 km/h, and the other half at a speed of 5 km/h. Vasya walks half the time at a speed of 4 km/h, and the other half at a speed of 5 km/h. They both leave the house at the same time. We need to determine who will arrive first.

Solution

To solve this problem, we can compare the distances covered by Vasya and Kolya.

Let's assume the total distance to Sasha's house is D km.

Kolya walks half the distance at a speed of 4 km/h, which means he covers D/2 km in (D/2) / 4 = D/8 hours.

Kolya then walks the other half of the distance at a speed of 5 km/h, which means he covers D/2 km in (D/2) / 5 = D/10 hours.

Therefore, Kolya's total travel time is (D/8) + (D/10) = (5D + 4D) / 40 = 9D / 40 hours.

Vasya walks half the time at a speed of 4 km/h, which means he covers (D/2) * (4/4) = D/2 km.

Vasya then walks the other half of the time at a speed of 5 km/h, which means he covers (D/2) * (5/5) = D/2 km.

Therefore, Vasya's total distance covered is D/2 + D/2 = D km.

Since both Kolya and Vasya leave the house at the same time, we can compare their travel times to determine who will arrive first.

If Kolya's travel time (9D / 40) is less than Vasya's travel time (D), then Kolya will arrive first. Otherwise, Vasya will arrive first.

Let's calculate the values and determine the result.

Calculation

Let's assume the total distance to Sasha's house is D km.

Kolya's travel time: (9D / 40) hours Vasya's travel time: D hours

To determine who will arrive first, we need to compare the travel times.

If (9D / 40) < D, then Kolya will arrive first. If (9D / 40) >= D, then Vasya will arrive first.

Result

To determine who will arrive first, we need to compare the travel times of Kolya and Vasya.

If (9D / 40) < D, then Kolya will arrive first. If (9D / 40) >= D, then Vasya will arrive first.

Please note that the specific value of D is not provided in the question, so we cannot determine the exact result. However, based on the given information, we can conclude that either Kolya or Vasya will arrive first depending on the value of D.