Respuesta :
Answer:
Total time taken by walking, running and cycling = 22 minutes.
Step-by-step explanation:
Let the speed of walking = x
As given,
The distance of walking = 1
Now,
As [tex]Time = \frac{Distance }{Speed}[/tex]
⇒ Time traveled by walking = [tex]\frac{1}{x}[/tex]
Now,
Given that - He runs twice as fast as he walks
⇒Speed of running = 2x
Also given distance traveled by running = 1
Time traveled by running = [tex]\frac{1}{2x}[/tex]
Now,
Given that - he cycles one and a half times as  fast as he runs.
⇒Speed of cycling =  [tex]\frac{3}{2}[/tex] (2x) = 3x
Also given distance traveled by cycling = 1
Time traveled by cycling = [tex]\frac{1}{3x}[/tex]
Now,
Total time traveled = Time traveled by walking + running + cycling
                = [tex]\frac{1}{x}[/tex] +  [tex]\frac{1}{2x}[/tex] + [tex]\frac{1}{3x}[/tex]
                = [tex]\frac{6+3+2}{6x} = \frac{11}{6x}[/tex]
If he cycled the three mile , then total time taken = [tex]\frac{1}{3x}[/tex] + [tex]\frac{1}{3x}[/tex] + [tex]\frac{1}{3x}[/tex] = x
Given,
He takes ten minutes longer than he would do if he cycled the three miles
⇒x + 10 = [tex]\frac{11}{6} x[/tex]
⇒[tex]x - \frac{11}{6} x = -10[/tex]
⇒[tex]-\frac{5}{6}x = -10[/tex]
⇒x = [tex]\frac{60}{5}[/tex] = 12
⇒x = 12
∴ we get
Total time traveled by walking + running + cycling = [tex]\frac{11}{6} x = \frac{11}{6} (12) = 11 (2) = 22[/tex] min
