SOLUTION: Ching leaves San Francisco and travels toward Los Angeles at 50 mi/h. An hour later, Phil leaves Los Angeles and travels toward San Francisco at 60 mi/h. If the two cities are 380

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Question 92458: Ching leaves San Francisco and travels toward Los Angeles at 50 mi/h. An hour later, Phil leaves Los Angeles and travels toward San Francisco at 60 mi/h. If the two cities are 380 miles apart, how many hours will it take for Ching to meet Phil?
Found 2 solutions by lailai15, Edwin McCravy:
Answer by lailai15(1) About Me  (Show Source):
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
`
lailai15(1)'s answer, 3,000, is utterly ridiculous!
`
Solution by Edwin McCravy: 

Ching leaves San Francisco and travels toward Los Angeles at 50 mi/h. An hour
later, Phil leaves Los Angeles and travels toward San Francisco at 60 mi/h. If
the two cities are 380 miles apart, how many hours will it take for Ching to
meet Phil?

You can do it in your head, but I'll do it both the "in your head" way as well
as the algebraic way:

You can do it in your head this way:

When Phil leaves, Ching is already 50 miles down the road, and is now only 330
miles from Phil.  Their rate of approach is then 60+50 or 110 mi/h, so at that
rate it'll obvously take Phil 3 hours to meet Ching.  But the problem asks how long will it will take for Ching to meet Phil, not how long it will take Phil to meet Ching.  Ching has traveled 1 hour more than Phil, so we can say:

It will take 3 hours for Phil to meet Ching from the later time Phil started.
It will take 4 hours for Ching to meet Phil from the earlier time Ching started. 

Algebraic method
Make this chart:

         DISTANCE   RATE     TIME
Ching    
Phil                              

Let x be the number of hours it will take Ching to meet Phil from the earlier
time Ching started. So put x for Ching's time:

         DISTANCE   RATE     TIME
Ching                          x                          
Phil                              

Phil started an hour later than Ching, so Phil's time is 1 hour less
than Ching's time, so put x-1 for Phil's time.

         DISTANCE   RATE     TIME
Ching                          x                          
Phil                          x-1 

Fill in their rates which are given as 50 and 60 mi/h


         DISTANCE   RATE     TIME
Ching                50        x                          
Phil                 60       x-1 

Now use DISTANCE = RATE × TIME to fill in the distances.

         DISTANCE   RATE     TIME
Ching       50x      50        x                          
Phil      60(x-1)    60       x-1 

We make the equation by reasoning that when they meet, together
they have covered the entire 380 mile road between the two cities.
Therefore the sum of their distances must equal 380 miles:

 Ching's distance + Phil's distance = 380 miles

        50x       +    60(x-1)      = 380              

Solve that and you'll get x = 4 hours from the time Ching started,
(which is, of course, 3 hours after Phil started.)

Edwin