Respuesta :
Answer:
The speed of faster cyclist is 85.6 m/h
The speed of slower cyclist is 78.6 m/h
Step-by-step explanation:
Given as :
The total distance between two cyclist = d = 123 miles
The Time taken by cyclist to move apart = t = 3 hours
Let The speed of faster cyclist = s miles per hour
And The speed of slower cyclist = (s - 7) miles per hour
Now, According to question
Time = [tex]\dfrac{\textrm distance}{\textrm speed}[/tex]
So, 3 = [tex]\dfrac{123}{s}[/tex] + [tex]\dfrac{123}{s - 7}[/tex]
Or, [tex]\dfrac{3}{123}[/tex] = [tex]\dfrac{1}{s}[/tex] + [tex]\dfrac{1}{s-7}[/tex]
Or, [tex]\dfrac{1}{41}[/tex] = [tex]\dfrac{s + (s - 7)}{s(s -7)}[/tex]
Or, s(s - 7) = 41 (2 s - 7)
Or, s² - 7 s = 82 s - 287
Or, s² - 7 s - 82 s + 287 = 0
Or, s² - 89 s + 287 = 0
Now, Solving this quadratic equation
s = [tex]\dfrac{- b\pm \sqrt{b^{2} - 4\times a\times c}}{2\times a}[/tex]
Or, s = [tex]\dfrac{- (-89)\pm \sqrt{(-89)^{2} - 4\times 1\times 287}}{2\times 1}[/tex]
Or, s = [tex]\frac{89+82.2}{2}[/tex] , [tex]\frac{89-82.2}{2}[/tex]
∴ speed = 85.6 m/h , 3.4 m/h
Here we consider 85.6 m/h
So, The speed of faster cyclist = s = 85.6 m/h
And The speed of slower cyclist = s - 7 = 85.6 - 7 = 78.6 m/h
Hence,The speed of faster cyclist is 85.6 m/h
And The speed of slower cyclist is 78.6 m/h Answer
