Question 173469
For both of them, {{{d = r*t}}}, where
{{{d}}}= distance
{{{r}}}= rate
{{{t}}}= time
So, for Carlos,
{{{d[c] = r[c]*t[c]}}}
And for Juanita,
{{{d[j] = r[j]*t[j]}}}
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The chart would look like this:
-------------------------------
Distances  --  rates  --  times
-------------------------------
 -- d[c] --  -- r[c] -- -- t[c]
 -- d[j] --  -- r[j] -- -- t[j]
--------------------------------
Now I can repace some of these variables
with things that I know about them
For instance, {{{d[c] = d[j]}}} because 
the distance is from LA to the place
where they meet. I'll call them both {{{d}}}
-------------------------------
Distances  --  rates  --  times
-------------------------------
 -- d --  -- r[c] --  -- t[c]
 -- d --  -- r[j] --  -- t[j]
--------------------------------
Carlos travels 50 mi/hr and Juanita travels 60 mi/hr, so
-------------------------------
Distances  --  rates  --  times
-------------------------------
 -- d --  -- 50 --     -- t[c]
 -- d --  -- 60 --     -- t[j]
--------------------------------
Juanita leaves LA an hour later, so she has to cover the same 
distance in 1 hour less time, so
-------------------------------
Distances  --  rates  --  times
-------------------------------
 -- d --    -- 50 --    --t[c]
 -- d --    -- 60 --    --t[c] - 1
--------------------------------
Now I can use this to find out when Juanita will pass Carlos.
The problem doesn't ask for it, but I'll do the algebra
{{{d = r*t}}} for both of them, so
(1) {{{d = 50t[c]}}}
{{{d = 60*(t[c] - 1)}}}
(2) {{{d = 60t[c] - 60}}}
The {{{d}}}s are the same in (1) and (2), 
so I'll set them equal to eachother
(3) {{{50t[c] = 60t[c] - 60}}}
{{{10t[c] = 60}}}
{{{t[c] = 6}}}
And, since {{{t[j] = t[c] - 1}}},
{{{t[j] = 6 - 1}}}
{{{t[j] = 5}}}
Carlos left LA at 8AM, so 6 hours later, 
it would have been 2PM
Juanita left LA at 9AM, so 5 hours later,
It would have been 2PM, which is when she passed him
check answer:
The distances must be the same, so
(1) {{{d = 50t[c]}}}
{{{d = 50*6}}}
{{{d = 300}}} mi
(2) {{{d = 60t[c] - 60}}}
{{{d = 60*6 - 60}}}
{{{d = 360 - 60}}}
{{{d = 300}}} mi
OK