Question

Два велосипедиста выехали одновременно навстречу друг другу из пунктов А и В, расстояние между которыми 24 км, и встретились через 1 ч 20 мин. Первый прибыл в пункт В на 36 мин раньше, чем второй в пункт А. Найдите скорость каждого велосипедиста. Только по подробнее и уравнение и сами логические рассуждения

Answer 1

Ответ:

1ч 20м=1 20/60=1 1/3=4/3ч

24:4/3=24*3/4=6*3=18 км/ч-скорость сближения

36м=36/60=6/10=0,6ч

х-скорость медленного

18-х-скорость быстрого

24/х-24(18-х)=0,6 разделим на 0,6

40/х-40(18-х)=1

40/х-40(18-х)-1=0 умножим на х(18-х)=18х-х²

40(18-х)-40х-(18х-х²)=0

720-40х-40х-18х+х²=0

х²-98х+720=0

D= (-98)² - 4·1·720 = 9604 - 2880 = 6724

x1 = (98 + √6724)/(2*1) = (98 + 82)/2 = 180/2 = 90- не подходит , т.к. скорость 2го будет отрицательной

x1 = (98 - √6724)/(2*1) = (98- 82)/2 = 16/2 = 8 км/ч- скорость медленного

18-18=10 км/ч-скорость быстрого

Answer 2

#### Problem Analysis We have two cyclists starting simultaneously from points A and B, which are 24 km apart. They meet after 1 hour and 20 minutes. The first cyclist arrives at point B 36 minutes earlier than the second cyclist arrives at point A. We need to find the speed of each cyclist. #### Solution Let's assume the speed of the first cyclist is **v1** km/h and the speed of the second cyclist is **v2** km/h. To solve this problem, we can use the formula: **distance = speed × time**. ##### Distance traveled by the first cyclist: The first cyclist travels from point A to the meeting point, which is 24 km away. The time taken is 1 hour and 20 minutes, which is equal to 1.33 hours. Therefore, the distance traveled by the first cyclist is **24 km**. ##### Distance traveled by the second cyclist: The second cyclist travels from point B to the meeting point, which is also 24 km away. The time taken is 1 hour and 20 minutes, which is equal to 1.33 hours. Therefore, the distance traveled by the second cyclist is **24 km**. ##### Time taken by the first cyclist: The first cyclist takes 1 hour and 20 minutes to reach the meeting point. This is equal to 1.33 hours. ##### Time taken by the second cyclist: The second cyclist takes 1 hour and 20 minutes to reach the meeting point. This is equal to 1.33 hours. ##### Time taken by the first cyclist to reach point B: The first cyclist arrives at point B 36 minutes earlier than the second cyclist arrives at point A. This is equal to 0.6 hours. Therefore, the time taken by the first cyclist to reach point B is **1.33 - 0.6 = 0.73 hours**. Now, we can use the formula **distance = speed × time** to find the speeds of the cyclists. ##### Speed of the first cyclist: The distance traveled by the first cyclist is 24 km, and the time taken is 0.73 hours. Therefore, the speed of the first cyclist is **24 km / 0.73 hours**. ##### Speed of the second cyclist: The distance traveled by the second cyclist is 24 km, and the time taken is 1.33 hours. Therefore, the speed of the second cyclist is **24 km / 1.33 hours**. #### Calculation Let's calculate the speeds of the cyclists using the given values: Speed of the first cyclist = **24 km / 0.73 hours** = 32.88 km/h Speed of the second cyclist = **24 km / 1.33 hours** = 18.05 km/h #### Answer The speed of the first cyclist is approximately **32.88 km/h**, and the speed of the second cyclist is approximately **18.05 km/h**. Please note that these values are approximate due to rounding. #### Logical Reasoning To solve this problem, we used the formula **distance = speed × time**. We considered the distances traveled by each cyclist, the time taken by each cyclist, and the time difference between the first cyclist reaching point B and the second cyclist reaching point A. By setting up equations using these values, we were able to find the speeds of the cyclists.