SOLUTION: At the beginning of a walk, Roberto and Juanita are 2.2 miles apart. If they leave at the same time and walk in the same direction, Roberto overtakes Juanita in 11 hours. If they w

Algebra ->  Equations -> SOLUTION: At the beginning of a walk, Roberto and Juanita are 2.2 miles apart. If they leave at the same time and walk in the same direction, Roberto overtakes Juanita in 11 hours. If they w      Log On


   

Question 1004298: At the beginning of a walk, Roberto and Juanita are 2.2 miles apart. If they leave at the same time and walk in the same direction, Roberto overtakes Juanita in 11 hours. If they walk towards each other, they meet in 1 hour. What is Roberto speed? What is Juanita speed?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let d%5B1%5D+ = distance that Roberto walks until they
meet when walking in the same direction
+d%5B1%5D+-+2.2+ = the distance that Juanita walks
---------------------------------------
Roberto's equation:
(1) +d%5B1%5D+=+s%5B1%5D%2A11+
Juanita's equation:
(2) +d%5B1%5D+-+2.2+=+s%5B2%5D%2A11+
---------------------
Now let +d%5B2%5D+ = distance roberto walks until they
meet when walking towards eachother
+2.2+-+d%5B2%5D+ = the distance Juanita walks
------------------------------------
Roberto's equation:
(3) +d%5B2%5D+=+s%5B1%5D%2A1+
Juanita's equation:
(4) +2.2+-+d%5B2%5D+=+s%5B2%5D%2A1+
-----------------------
Substitute (1) into (2)
(2) +11%2As%5B1%5D+-+2.2+=+11%2As%5B2%5D+
(2) +11%2A%28+s%5B1%5D+-+s%5B2%5D+%29+=+2.2+
(2) +s%5B1%5D+-+s%5B2%5D+=+.2+
-----------------------
Substitute (3) into (4)
(4) +2.2+-s%5B1%5D+=+s%5B2%5D%2A1+
(4) +s%5B1%5D+%2B+s%5B2%5D+=+2.2+
-----------------------
Add (2) and (4)
(4) +s%5B1%5D+%2B+s%5B2%5D+=+2.2+
(2) +s%5B1%5D+-+s%5B2%5D+=+.2+
---------------------
+2%2As%5B1%5D+=+2.4+
+s%5B1%5D+=+1.2+
and
(4) +s%5B1%5D+%2B+s%5B2%5D+=+2.2+
(4) +s%5B2%5D+%2B1.2+=+2.2+
(4) +s%5B2%5D+=+1+
----------------------
Roberto's speed is 1.2 mi/hr
Juanita's speed is 1 mi/hr
----------------------
check:
(1) +d%5B1%5D+=+s%5B1%5D%2A11+
(1) +d%5B1%5D+=+1.2%2A11+
(1) +d%5B1%5D+=+13.2+
and
(2) +d%5B1%5D+-+2.2+=+s%5B2%5D%2A11+
(2) +13.2+-+2.2+=+s%5B2%5D%2A11+
(2) +11%2As%5B2%5D+=+11+
(2) +s%5B2%5D+=+1+
------------------
(3) +d%5B2%5D+=+s%5B1%5D%2A1+
(3) +d%5B2%5D+=+1.2%2A1+
(3) +d%5B2%5D+=+1.2+
and
(4) +2.2+-+d%5B2%5D+=+s%5B2%5D%2A1+
(4) +2.2+-+1.2+=+s%5B2%5D%2A1+
(4) +s%5B2%5D+=+1+
OK