Question

Два велосипедиста выхали одновременно из пункта А, первый со скоростью 24 км/ч, второй - 18 км/ч. Спустя час вслед за ними выехал автомобиль, который обогнал второго велосипедиста на 10 мин раньше, чем второго. Найдите скорость автомобиля.

Answer 1

Пусть х - скорость автомобиля. у - время движения второго велосипедиста до момента, когда его нагнал автомобиль. Тогда у + (1/6) - время движения первого велосипедиста до момента, когда его нагнал автомобиль.

Из условия равенства путей получим два уравнения:

18у = (у-1)х                                     18у = (у-1)х

24(у+ (1/6)) = (у+ (1/6) -1)х          24у + 4 = (у - (5/6))х

Поделив уравнения получим пропорцию:

$\frac{18y}{24y+4}\ =\ \frac{y-1}{y-\frac{5}{6}},\ \ \ \ 18y^2-15y=24y^2-20y-4,\ \ \ \ 6y^2-5y-4=0$

D= 121,    y = (5+11)/12 = 4/3

Подставим в 1 уравнение системы и найдем х:

24 = х/3    х = 72.

Ответ: 72 км/ч

Answer 2

Problem Analysis

We are given that two cyclists start simultaneously from point A. The first cyclist has a speed of 24 km/h, while the second cyclist has a speed of 18 km/h. An hour later, a car starts from point A and overtakes the second cyclist 10 minutes before overtaking the first cyclist. We need to find the speed of the car.

Solution

Let's assume that the car's speed is x km/h.

We know that the second cyclist is overtaken by the car 10 minutes before the first cyclist. This means that the car takes 10 minutes less than the first cyclist to reach the second cyclist.

We can calculate the time taken by the first cyclist to reach the second cyclist using the formula:

time = distance / speed

The distance covered by the first cyclist in one hour is 24 km, and the distance covered by the second cyclist in one hour is 18 km. Therefore, the distance between the two cyclists is 24 - 18 = 6 km.

The time taken by the first cyclist to cover this distance is:

time = distance / speed = 6 km / 24 km/h = 0.25 hours

Since the car overtakes the second cyclist 10 minutes before overtaking the first cyclist, the time taken by the car to cover the distance between the two cyclists is:

time = 0.25 hours - 10 minutes = 0.25 hours - (10/60) hours = 0.25 - 0.1667 hours = 0.0833 hours

Now, we can calculate the speed of the car using the formula:

speed = distance / time

The distance covered by the car in 0.0833 hours is 6 km. Therefore, the speed of the car is:

speed = 6 km / 0.0833 hours = 72 km/h

So, the speed of the car is 72 km/h.

Answer

The speed of the car is 72 km/h.