Question

5

Answer 1

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 $Time = \frac{Distance }{Speed}$

⇒ Time traveled by walking = $\frac{1}{x}$

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 = $\frac{1}{2x}$

Now,

Given that - he cycles one and a half times as  fast as he runs.

⇒Speed of cycling =  $\frac{3}{2}$ (2x) = 3x

Also given distance traveled by cycling = 1

Time traveled by cycling = $\frac{1}{3x}$

Now,

Total time traveled = Time traveled by walking + running + cycling

                                = $\frac{1}{x}$ +  $\frac{1}{2x}$ + $\frac{1}{3x}$

                                = $\frac{6+3+2}{6x} = \frac{11}{6x}$

If he cycled the three mile , then total time taken = $\frac{1}{3x}$ + $\frac{1}{3x}$ + $\frac{1}{3x}$ = x

Given,

He takes ten minutes longer than he would do if he cycled the three miles

⇒x + 10 = $\frac{11}{6} x$

⇒$x - \frac{11}{6} x = -10$

⇒$-\frac{5}{6}x = -10$

⇒x = $\frac{60}{5}$ = 12

⇒x = 12

∴ we get

Total time traveled by walking + running + cycling = $\frac{11}{6} x = \frac{11}{6} (12) = 11 (2) = 22$ min