SOLUTION: Ben and Peter start off together on a 20 km hike. Ben walks 4 times as fast as Peter, and when he comes to the end of the hike he turns around and walks to meet Peter. How far, in

Question 1104965: Ben and Peter start off together on a 20 km hike. Ben walks 4 times as fast as Peter, and when he comes to the end of the hike he turns around and walks to meet Peter. How far, in km, has Peter walked when they meet?
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = Peter's speed in km/hr
= Ben's speed in km/hr
Let = Peter's time in hrs to walk to the
point where he is met by Ben
Let = distance in km that Peter travels
until he meets Ben
---------------------------------------
Peter's equation:
(1)
Ben's equation:
(2)
----------------------------
(2)
(2)
----------------------------
(2)
(2)
(2)
(2)
Peter has walked 8 km when they meet
--------------------------------------
check:
(2)
(2)
(2)
(2)
OK

Answer by ikleyn(52921) (Show Source): You can put this solution on YOUR website!
.
You can solve it MENTALLY.

When Ben and Peter will meet each other, they will cover together the distance of 20 kilometers twice. In other words, they will cover the total distance of 2*20 = 40 kilometers. Of these 40 kilometers, more faster will cover four parts of the total, while the slower will cover only 1 part. In all, you have 5 parts in 40 kilometers, so each part is 8 kilometers. Thus Ben will cover 4*8 = 32 kilometers, while Peter will cover only 8 kilometers.

Solved.

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