Two men running

Adam and Bob have exact speeds for walking and running – neither Adam outwalks Bob, nor Bob outruns Adam.

But for a given distance, Adam runs half the time, then walks another half. Bob runs half the distance, then walks another half.

If they were to compete, which distance would Adam win at, and which distances would Bob be the winner at?

Answer:

Let running speed = r, walking speed = w
total distance x = x1 + x2
total time T = t1 + t2

for Adam:
t = T/2
x1 = rT/2
x2 = wT/2
xa = T * (w+r)/2 ——–1

for Bob:
t1 = x/2r
t2 = x/2w
T = t1 + t2
xb = T * 2rw/(w+r) ——–2

divide 1 by 2 ->

xa/xb = (w^2 + 2wr + r^2) / 4wr ;r > w > 0
Hance, xa/xb is always > 1

so Adam always wins!

Alternate solution: (by another user on source site)

simpler question is… can Adam cover more than 1/2 of distance in 1/2 of the time… if true, Adam always win… since both of them walk for the rest

We know running is faster than walking… so to cover 1/2 of distance by running and walking… running takes less time… therefore it will take less than 1/2 of the time

Now you let Adam run for 1/2 of the time, it will surpass 1/2 the distance

So Adam always win

via Two men running | TechInterviews.

Tags: , ,


Did You Enjoy This Post?

Subscribe to our blog through our RSS feed or email to receive updates on more posts like this.post on your favourite social networking or media site to let others know about this post. Help us generate more buzz by submitting/voting for this post with the following buttons.

One Response to “Two men running”

  1. solidusse says:

    Nice article. last thirty days I uncovered this website and desired to permit you be conscious that i’ve been gratified, heading via your site’s posts. I should certainly be signing equally as much as the RSS feed and should certainly wait around for another post. best Regards, Mateus

Leave a Reply











request new questions/article: send email to freequestionbank at gmail dot com