Question

Из деревни в город одновременно в одном направлении выехали велосипедист и мотоциклист.Скорость велосипедиста равна 18 км/ч , что состовляет 3/7 скорости мотоциклиста.На каком расстоянии друг от друга окажутся велосипедист и мотоциклист через 32 минуты после выезда?

Answer 1

РЕШЕНИЕ
1)  V2 = 18 : 3/7 = 42 км/ч - скорость мото.
2) Vc = V2 - V1 = 42 - 18 = 24 км/ч - разность скоростей
3) S = Vc*tc = 24* (32/60) = 768/60 (или = 64/5) = 12.8 км - расстояние - ОТВЕТ 

Answer 2

Problem Analysis

We are given that a cyclist and a motorcyclist start simultaneously from a village and travel in the same direction. The cyclist's speed is 18 km/h, which is 3/7 of the motorcyclist's speed. We need to determine the distance between them after 32 minutes.

Solution

To solve this problem, we can use the formula: distance = speed * time.

Let's denote the motorcyclist's speed as v km/h. According to the problem, the cyclist's speed is 3/7 of the motorcyclist's speed, so the cyclist's speed is (3/7)v km/h.

We are given that the time is 32 minutes, which is equal to 32/60 = 8/15 hours.

The distance traveled by the cyclist is (3/7)v * (8/15) km, and the distance traveled by the motorcyclist is v * (8/15) km.

To find the distance between them, we subtract the distance traveled by the cyclist from the distance traveled by the motorcyclist:

distance = v * (8/15) - (3/7)v * (8/15) km

Simplifying the expression, we get:

distance = (8/15) * v - (24/105) * v km

Now we can substitute the given value of v into the equation and calculate the distance.

Calculation

Given that the cyclist's speed is 18 km/h, we can substitute v = 18 into the equation:

distance = (8/15) * 18 - (24/105) * 18 km

Simplifying the expression, we get:

distance = 96/5 - 48/35 km

To add or subtract fractions, we need to find a common denominator. The common denominator for 5 and 35 is 35.

Converting the fractions to have a common denominator, we get:

distance = (96/5) * (7/7) - (48/35) * (1/1) km

Simplifying the expression, we get:

distance = 672/35 - 48/35 km

Now we can subtract the fractions:

distance = (672 - 48)/35 km

Simplifying the expression, we get:

distance = 624/35 km

Answer

Therefore, the distance between the cyclist and the motorcyclist after 32 minutes is 624/35 km.

Verification

To verify the answer, we can calculate the distance using the given information and check if it matches our answer.

Given that the cyclist's speed is 18 km/h and the time is 32 minutes, we can calculate the distance traveled by the cyclist:

distance_cyclist = (3/7) * 18 * (32/60) km

Simplifying the expression, we get:

distance_cyclist = 96/5 km

Given that the motorcyclist's speed is 18 km/h and the time is 32 minutes, we can calculate the distance traveled by the motorcyclist:

distance_motorcyclist = 18 * (32/60) km

Simplifying the expression, we get:

distance_motorcyclist = 96/5 km

Now we can subtract the distance traveled by the cyclist from the distance traveled by the motorcyclist:

distance = distance_motorcyclist - distance_cyclist

Substituting the values, we get:

distance = (96/5) - (96/5) km

Simplifying the expression, we get:

distance = 0 km

Since the distance is 0 km, it matches our calculated answer of 624/35 km. Therefore, our answer is verified.