Question

Two cyclists start at the same point and travel in opposite directions. One cyclist travels 7 mi/h slower than the other. If the two cyclists are 123 miles apart after 3 hours, what is the rate of each cyclist?

Answer 1

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 = $\dfrac{\textrm distance}{\textrm speed}$

So, 3 = $\dfrac{123}{s}$ + $\dfrac{123}{s - 7}$

Or, $\dfrac{3}{123}$ = $\dfrac{1}{s}$ + $\dfrac{1}{s-7}$

Or, $\dfrac{1}{41}$ = $\dfrac{s + (s - 7)}{s(s -7)}$

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 = $\dfrac{- b\pm \sqrt{b^{2} - 4\times a\times c}}{2\times a}$

Or, s = $\dfrac{- (-89)\pm \sqrt{(-89)^{2} - 4\times 1\times 287}}{2\times 1}$

Or, s = $\frac{89+82.2}{2}$ ,  $\frac{89-82.2}{2}$

∴ 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