Question

Із двох міст назустріч один одному виїхали велосипедист і мотоцикліст. Швидкість мотоцикліста дорівнює ​​ 43(целых) 2/15 км/год, а швидкість велосипедиста в 3 (целых) 1/2 рази менша від швидкості мотоцикліста. Через скільки годин після початку руху вони зустрінуться, якщо відстань між містами становить 139(целых) ​​ 1/2 км?

Answer 1

Пошаговое объяснение:

1) 43 2/15 : 3 1/2 = 647/15 : 7/2 = 647/15 * 2/7 = 1294/105 = 12 34/105 (км/ч) - скорость велосипедиста

2) 43 2/15 + 12 34/105 = 43 14/105 + 12 34/105 = 55 48/105 (км/ч) - скорость сближения велосипедиста и мотоциклиста

3) 139 1/2 : 55 48/105 = 279/2 : 5823/105 = 279/2 * 105/5823 = 29295/11646 = 2 6003/11646 = 2 667/1294 или ≈ 2,5 (часа) - они встретятся

Answer 2

To find out when the cyclist and the motorcyclist will meet, we need to calculate the time it takes for them to cover the distance between the two cities.

Let's first convert the given speeds into fractions:

- The speed of the motorcyclist is 43 2/15 km/h. - The speed of the cyclist is 3 1/2 times slower than the speed of the motorcyclist.

Now, let's calculate the speed of the cyclist:

Speed of the cyclist = (3 1/2) * (43 2/15) km/h

To multiply mixed numbers, we need to convert them into improper fractions:

Speed of the cyclist = (7/2) * (657/15) km/h

To multiply fractions, we multiply the numerators and denominators:

Speed of the cyclist = (7 * 657) / (2 * 15) km/h

Simplifying the fraction:

Speed of the cyclist = 4599/30 km/h

Now that we have the speeds of both the motorcyclist and the cyclist, we can calculate the time it takes for them to meet.

Let's use the formula: time = distance / speed

The distance between the two cities is given as 139 1/2 km.

For the motorcyclist: Time taken by the motorcyclist = (139 1/2) / (43 2/15) hours

For the cyclist: Time taken by the cyclist = (139 1/2) / (4599/30) hours

To add or subtract mixed numbers, we need to convert them into improper fractions:

Time taken by the motorcyclist = (279/2) / (657/15) hours

Time taken by the cyclist = (279/2) / (4599/30) hours

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:

Time taken by the motorcyclist = (279/2) * (15/657) hours

Time taken by the cyclist = (279/2) * (30/4599) hours

Now, let's calculate the values:

Time taken by the motorcyclist = (279 * 15) / (2 * 657) hours

Time taken by the cyclist = (279 * 30) / (2 * 4599) hours

Simplifying the fractions:

Time taken by the motorcyclist = 1395/4382 hours

Time taken by the cyclist = 1395/3066 hours

To find the time it takes for them to meet, we need to find the least common multiple (LCM) of the two denominators: 4382 and 3066.

The LCM of 4382 and 3066 is 134,383,812.

Now, let's convert the fractions to have the same denominator:

Time taken by the motorcyclist = (1395/4382) * (134383812/134383812) hours

Time taken by the cyclist = (1395/3066) * (134383812/134383812) hours

Calculating the values:

Time taken by the motorcyclist = 187,065,390/134,383,812 hours

Time taken by the cyclist = 187,065,390/134,383,812 hours

Therefore, the cyclist and the motorcyclist will meet approximately after 1.393 hours (rounded to three decimal places) from the start of their journey.

Note: The calculations have been done based on the given information and the assumption that the speeds remain constant throughout the journey.