Walk The Talk!

let my speed be s. The speed of the walkway be w.

1)Walking in the correct direction d = (s + w)(162 seconds)

2) Walking in the wrong direction d = (s – w)(810 seconds)

Multiply first equation by 5 and then subtract second equation from first.

4d = (w) (1620 seconds)

d/w = 1620/4 = 405 seconds.

I have a ratio based method of solving the same problem.

Now, the distance remains constant both ways, be it with the motion of the walkway or against. Thus 162(m+w)=810(m-w), assuming off course that the speeds of the man and the walkway are m and w respectively. Now since the ratio of the two times are 1:5 thus speed ratios must be 5:1 as speed and time are inversely proportional for constant distance. The two values which will satisfy the equation would be 3 and 2 as 3+2=5 and 3-2=1. Now, when the the mans speed is 0, then he would be effectively moving at the walkway's speed which is essentially 2/5th of the total initial speed(which was 5). Since the speed is 2/5th of the value, the time will be 5/2th of the original time which in this case would 5/2*162 which is 405.

let my speed = v. let walkway stream speed = a. let walkway be x distance. we know speed = distance/time let time for first be t1, viz 162 let time for second be t2 viz 162 times 5 thus, speed * time = distance.

According to the question: 1. (v+a) = x/t1 & 2. (v-a) = x/t2 we now have 2 eq. and need to find 'a' and/or 'v' in terms 'x' thus the problem is solved.

Let the guy speed be Sg and the walkway be Sw. We have that the relative total speed of the system, when the guy is walking towards, is S = Sg + Sw, and when the guy is walking in the opposite way, is S = Sq - Sw.

Given that the general formula for speed is S = D / T where S is speed, D is distance and T is time, walking towards gives us the formula Sg + Sw = D / 162, and walking backwards gives us the formula Sg - Sw = D / 810.

Working with the walkway speed only, we have that (D/162) - Sw = (D/810) + Sw. Solving this equation, we get that our constant D = 405Sw.

Switching the speed formula to isolate the distance, we get D = T * S, which is exactly what we have there, D = 405 * Sw, so, the time the walkway takes to move that distance D is 405s.