SOLUTION: Leona Jackson and Sam Peterson love to walk. Leona walks 5 miles per hour. Sam walks 6 miles per hour. Assume they start walking from the same place and walk in a straight line. Sa

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Question 1094187: Leona Jackson and Sam Peterson love to walk. Leona walks 5 miles per hour. Sam walks 6 miles per hour. Assume they start walking from the same place and walk in a straight line. Sam starts 1/2 hour after Leona. How long will it take Sam to meet Leona? How many miles would each have walked?
Found 3 solutions by greenestamps, josgarithmetic, ikleyn:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!

(1) When Sam starts walking, how far has Leona walked?
(2) At what rate does Sam catch up to Leona? That is, how many miles farther does he walk each hour?
(3) At the rate from question (2), how many hours does it take Sam to make up the distance from question (1)?

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
               SPEED       TIME           DISTANCE

LEONA           5          d%2F5               d

SAM             6          d%2F6               d

DIFFERENCE                 1%2F2

Leona spent more time walking the same distance d, which sam also walked.

highlight_green%28d%2F5-d%2F6=1%2F2%29
Solve for distance d, and use it to find the walking time each of Leona and Sam.

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
In half an hour, Leona walked 0.5*5 = 2.5 miles.

So, she was 2.5 miles ahead when Sam started his walk.

Each hour the distance between them decreases 6-5 = 1 miles.


So, initial distance of 2.5 miles between them decreases at the rate 1 mile per hour.


Hence, Sam will catch Leona in 2.5 hours after Sam's start.


There are many approaches and many ways of solving such problems.

See the lesson
    - Travel and Distance problems for two bodies moving in the same direction (catching up)
in this site.


Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the section "Word problems",  the topic "Travel and Distance problems".


Under this topic, I collected a unique set of various types of Travel and Distance problems for those who loves them.


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.