SOLUTION: help me set up this world problem: John left willie house driving toward the mountains one hour before Wilbur. Wilbur drove in the opposite direction going 12 km/h slower than

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Question 1093232: help me set up this world problem:
John left willie house driving toward the mountains one hour before Wilbur. Wilbur drove in the opposite direction going 12 km/h slower than john for one hour after which time there were 159 km apart. Find johns speed.
Found 3 solutions by ikleyn, josmiceli, greenestamps:
Answer by ikleyn(52809) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let J be john's speed, in km/h.

Then the Wilbur' speed is J-12 km/h.

In one hour John covered J kilometers, while Wilbour covered J-12 kilometers in opposite direction.


Hence, the distance between them in one hour is J + (J-12) = 2J-12.


From the other side, it is 159 km, according to the solution.


It gives you an equation

2J - 12 = 159.


The set up  is completed.


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To see many other samples, examples and solved problems of this kind, look into the lessons
    - Travel and Distance problems
    - Travel and Distance problems for two bodies moving in opposite directions
    - Travel and Distance problems for two bodies moving in the same direction (catching up)
in this site.



Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
First find John's head start in terms of miles
Let +s+ = John's speed in mi/hr
+d%5B1%5D+=+s%2A1+
------------------------
Start a stop watch when Wilbur leaves.
It will stop in 1 hr
Let +d+ = the distance in miles Wilbur travels
in the 1 hr on the stop watch
Wilbur's equation:
(1) +d+=+%28+s+-+12+%29%2A1+
John's equation:
(2) +%28+159+-+d+%29+-+d%5B1%5D+=+s%2A1+
-----------------------------
(2) +159+-+d+-+s%2A1+=+s%2A1+
(2) +159+-+d+=+2s+
(2) +d+=+159+-+2s+
and
(1) +d+=+s+-+12+
------------------------
Set (1) = (2)
+159+-+2s+=+s+-+12+
+3s+=+171+
+s+=+57+
John's speed is 57 mi/hr
------------------------
check answer:
(1) +d+=+s+-+12+
(1) +d+=+57+-+12+
(1) +d+=+45+ mi
and
(2) +159+-+d+-+s+=+s+
(2) +159+-+d+=+2%2A57+
(2) +d+=+159+-+114+
(2) +d+=+45+ mi
OK

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!

The first solution posted overlooked the fact that John traveled for 2 hours and Wilbur for only one hour. Other than that, it is a simpler approach than used in the second response.

Correcting the oversight in the first response, we have
John traveling for 2 hours at speed x;
Wilbur traveling for 1 hour at speed x-12; and
at the end they are 159 miles apart. So

2%28x%29+%2B+1%28x-12%29+=+159

And, as was said in the first response, you should be able to finish from there.