SOLUTION: Derick and Peter walk from point Y and Z, respectively walks toward each other at the same in constant speed. They meet the first time at a point that is eight miles away from Poin

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Question 618836: Derick and Peter walk from point Y and Z, respectively walks toward each other at the same in constant speed. They meet the first time at a point that is eight miles away from Point Y. They kept going without stop. As soon as one reach Y or Z, one returns in the same route. They meet the second time at a point five miles away from point Z. What is the distance between the two points that they met one another?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Derick and Peter walk from point Y and Z, respectively walks toward each other at the same in constant speed.
They meet the first time at a point that is eight miles away from Point Y.
They kept going without stop. As soon as one reach Y or Z, one returns in the same route.
They meet the second time at a point five miles away from point Z.
What is the distance between the two points that they met one another?
:
y------------>8mi------5mi<--------z
:
Let d = distance from y to z
:
First meeting:
D walks 8 mi
P walks (d-8) mi
:
2nd meeting:
D walks: (d-8) + 5 = d-3 mi
P walks: 8 + (d-5) = d+3 mi
:
The relationship of the distances walked by the two boys is the same for each meeting.
therefore
8%2F%28%28d-8%29%29 = %28%28d-3%29%29%2F%28%28d%2B3%29%29
cross multiply
8(d+3) = (d-8)(d-3)
FOIL the right side
8d + 24 = d^2 - 3d - 8d + 24
Combine like terms on the right
0 = d^2 - 11d - 8d + 24 - 24
leaving
d^2 - 19d = 0
Factor
d(d-19) = 0
our solution
d = 19 mi from y to z
:
"What is the distance between the two points that they met one another?"
Assume this means how far from the 8mi from y to 5mi from z
(19-5) - 8 = 6 mi between the two points