Question

Велотуристы 2 ч ехали с одной скоростью, а затем снизили её и с меньшей скоростью ехали ещё 3 ч 20 мин. Найдите большую и меньшую скорости туристов, учитывая, что вместе эти скорости сотавляют 31 км/ч, а всего туристы проехали 82 км.

Answer 1

х-первоночальная скорость

у-сниженая скорость

2х+3,2у=82

х+у=31 (2х+2у=62)

82-62=4/3у(1,2ч)

у=20*3/4=15км/ч

х=31-15=16км/ч

Answer 2

Problem Analysis

We are given that two cyclists initially traveled at the same speed for 2 hours. Then, they reduced their speed and traveled for an additional 3 hours and 20 minutes. We need to find the greater and lesser speeds of the cyclists, given that their combined speeds add up to 31 km/h and they traveled a total distance of 82 km.

Solution

Let's assume the initial speed of both cyclists is x km/h. Since they traveled at the same speed for 2 hours, the distance covered by each cyclist during this time is 2x km.

Next, they reduced their speed and traveled for an additional 3 hours and 20 minutes, which is equivalent to 3.33 hours. Let's assume the reduced speed of one cyclist is y km/h. Therefore, the reduced speed of the other cyclist is (31 - y) km/h, as their combined speeds add up to 31 km/h.

During the reduced speed period, the distance covered by the first cyclist is 3.33y km, and the distance covered by the second cyclist is 3.33(31 - y) km.

The total distance covered by both cyclists is 82 km. Therefore, we can write the equation:

2x + 3.33y + 3.33(31 - y) = 82

Simplifying the equation:

2x + 3.33y + 103.23 - 3.33y = 82

2x + 103.23 = 82

2x = 82 - 103.23

2x = -21.23

x = -10.615

Since speed cannot be negative, we can ignore the negative value of x. Therefore, the initial speed of both cyclists is approximately 10.615 km/h.

To find the reduced speed of one cyclist, we substitute the value of x into the equation:

2(10.615) + 3.33y + 3.33(31 - y) = 82

21.23 + 3.33y + 103.23 - 3.33y = 82

21.23 + 103.23 = 82

3.33y = 82 - 124.46

3.33y = -42.46

y = -12.75

Again, we ignore the negative value of y. Therefore, the reduced speed of one cyclist is approximately 12.75 km/h.

Since the combined speeds of the cyclists add up to 31 km/h, the reduced speed of the other cyclist is (31 - 12.75) km/h, which is approximately 18.25 km/h.

Answer

Therefore, the greater speed of the cyclists is approximately 18.25 km/h, and the lesser speed is approximately 10.615 km/h.