Question

Из А в Б выехал велосипедист со скоростью 10 целых пять шестых км в час одновременно из В в том же нарвлении вышел турист скоростью в одну целую три восьмых раза меньше первого . Через сколько часов 1 догонит 2 если растояние от А до В 5 км

Answer 1

10 5/6:1 3/8=65/6:11/8=260/33=7 29/33 (км/ч) скорость туриста
10 5/6-7 29/33=10 55/66-7 58/66=9 121/66-7 58/66=2 63/66=2 21/22 (км/ч) скорость, с какой велосипедист догоняет туриста
5:2 21/22=5:65/22=22/13=1 9/13 (ч)
Ответ: велосипедист догонит туриста через 1 9/13 часа

Answer 2

Problem Analysis

We have two individuals, a cyclist and a tourist, starting from points A and B respectively. The cyclist has a speed of 10 5/6 km/h, while the tourist has a speed that is 1 3/8 times slower than the cyclist. We need to determine how many hours it will take for the tourist to catch up to the cyclist, given that the distance between points A and B is 5 km.

Solution

Let's start by calculating the speed of the tourist. We know that the tourist's speed is 1 3/8 times slower than the cyclist's speed. To find the tourist's speed, we can multiply the cyclist's speed by 1 3/8.

The cyclist's speed is 10 5/6 km/h. To convert this mixed fraction into an improper fraction, we multiply the whole number (10) by the denominator (6) and add the numerator (5). This gives us a total of 65/6 km/h.

Now, let's calculate the tourist's speed. We multiply the cyclist's speed (65/6 km/h) by 1 3/8.

(65/6 km/h) * (1 3/8) = (65/6 km/h) * (11/8)

To multiply fractions, we multiply the numerators (65 * 11) and the denominators (6 * 8).

(65/6 km/h) * (11/8) = (715/48 km/h)

So, the tourist's speed is 715/48 km/h.

Now that we have the speeds of both the cyclist and the tourist, we can determine the time it will take for the tourist to catch up to the cyclist.

Let's assume that the time it takes for the tourist to catch up to the cyclist is t hours.

The distance traveled by the cyclist in t hours is given by the formula: distance = speed * time.

The distance traveled by the cyclist is (65/6 km/h) * t.

The distance traveled by the tourist is (715/48 km/h) * t.

Since the distance between points A and B is 5 km, we can set up the equation:

(65/6 km/h) * t + 5 km = (715/48 km/h) * t

Now, we can solve this equation to find the value of t.

To solve the equation, we can multiply both sides by 48 to eliminate the denominators:

48 * [(65/6 km/h) * t + 5 km] = 48 * [(715/48 km/h) * t]

Simplifying the equation:

(48 * 65/6) * t + 48 * 5 = 715 * t

Now, we can solve for t:

(520/3) * t + 240 = 715 * t

Rearranging the equation:

(520/3) * t - 715 * t = -240

Combining like terms:

(520/3 - 715) * t = -240

Simplifying further:

(-175/3) * t = -240

To solve for t, we can multiply both sides by -3/175:

t = (-240) * (-3/175)

Simplifying the equation:

t = 12/7

Therefore, it will take approximately 1.71 hours for the tourist to catch up to the cyclist.

Note: The above solution assumes that both the cyclist and the tourist travel in a straight line from points A to B. It also assumes that their speeds remain constant throughout the journey.