Twelve soldiers had to get to a place twenty miles distant as quickly as possible and each had to arrive at the same time. They requisitioned the services of a man with a small car.

“Through this zone I can do a constant 20 miles an hour, but I cannot carry more than four men at a time. At what rate can you walk?”
“All of us can do a steady four miles an hour.”
“Very well, then I will go ahead with four men, drop them somewhere on the road to walk, then will pick up four more (who will already have started out), drop them also, and return for the last four. So all you have to do is keep walking while you are on your feet and I will do the rest.”

They started at noon and arrived safely, together, at the same time, according to plan.

What was the exact time they arrived?

Let the distance travelled by the car per group be x.

Therefore, distance walked is 20-x.

When the first group was dropped, distance walked by the other groups would have been 10-x/2, and total distance travelled by the car would have been x+x-10+x/2=5x/2-10.

So, we have

1/2(20-x)=1/5(5x/2-10)

Solving this equation we get x=12 miles

Distance walked is 20-12=8 miles.

So, total time will be 12/20+8/4=3/5+2=13/5=2.6 hours.

Posted by Sparsh on 2006-05-10 07:20:43