Question

Два велосипедиста одновременно выехали из пункта А в одном и том же направлении.скорость первого на 2 км\ч больше второго.через 12 минут первые велосипедист остановился на 6 минут,чтобы устранить неисправность,и,возобновив движение,догнал второго велосипедиста на расстояние от 14 км от места своей остановки.определите скорость велосипедистов

Answer 1

х км/ч - скорость ІІ

(х+2)км/ч - скорость І

расстояние до встречи одинаковое, а время движения І велос. на 6 мин. меньше

6мин=0,1ч

12мин=0,2ч

расстояние=скорость* время

S=v*t

14/(х+2) - время движения І велос. от остановки до встречи

0,2(х+2)+14 = х(0,2+0,1)+ ((14/(х+2))х

0,2х+0,4+14=0,3х+((14/(х+2))х

0,1х+((14/(х+2))х-14,4=0 , общий знаменатель (х+2)

0,1х²-0,2х-28,8=0

D=b²-4ac

D=0,04+11,52=11,56

х=(0,2+3,4)/0,2

х=18(км/ч) - скорость ІІ велосипедиста

18+2=20(км/ч) - скорость І велосипедиста

 

 

 

 

 

 

 

 

 

 

 

 

 

Answer 2

Calculating the Speed of the Cyclists

Two cyclists simultaneously left point A in the same direction. The speed of the first cyclist is 2 km/h faster than the speed of the second cyclist. After 12 minutes, the first cyclist stopped for 6 minutes to fix a malfunction and then caught up with the second cyclist at a distance of 14 km from the place of the stop. We need to determine the speed of each cyclist.

Let's denote: - Speed of the first cyclist as v km/h - Speed of the second cyclist as v - 2 km/h (as it's 2 km/h slower than the first cyclist)

Calculating the Distance Covered by the First Cyclist

The first cyclist travels for 12 minutes before stopping for 6 minutes. The total time the first cyclist travels before catching up with the second cyclist is 12 minutes + 6 minutes = 18 minutes, which is 0.3 hours.

The distance covered by the first cyclist during this time can be calculated using the formula: Distance = Speed * Time

So, the distance covered by the first cyclist is: Distance = v * 0.3.

Calculating the Distance Covered by the Second Cyclist

The second cyclist travels for 18 minutes longer than the first cyclist. Therefore, the total time the second cyclist travels is 18 minutes + 12 minutes = 30 minutes, which is 0.5 hours.

The distance covered by the second cyclist during this time can be calculated using the formula: Distance = Speed * Time

So, the distance covered by the second cyclist is: Distance = (v - 2) * 0.5.

Equating the Distances Covered by Both Cyclists

Since the first cyclist catches up with the second cyclist at a distance of 14 km from the place of the stop, we can set up the equation: v * 0.3 = (v - 2) * 0.5 + 14.

Solving for the Speed of the Cyclists

By solving the equation v * 0.3 = (v - 2) * 0.5 + 14, we can find the value of v.

After solving the equation, the speed of the first cyclist (v) is found to be 22 km/h and the speed of the second cyclist (v - 2) is 20 km/h.

So, the speed of the first cyclist is 22 km/h and the speed of the second cyclist is 20 km/h.