SOLUTION: Joe and Louis are making a drive from San Diego to Salt Lake City. After 4 hours of driving, they are 507 miles from Salt Lake City. Eight hours into their trip, they are only 26

Algebra ->  Graphs -> SOLUTION: Joe and Louis are making a drive from San Diego to Salt Lake City. After 4 hours of driving, they are 507 miles from Salt Lake City. Eight hours into their trip, they are only 26      Log On


   

Question 884300: Joe and Louis are making a drive from San Diego to Salt Lake City. After 4 hours of driving, they are 507 miles from Salt Lake City. Eight hours into their trip, they are only 267 miles away from their destination. Assume they averaged the same speed for the entire trip.
To write the expression, define a variable for the time they have been driving and use this variable to write an expression for the distance they are from Salt Lake City.
I need an expression for y = mx = b
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+y+=+m%2Ax+%2B+b+
The slope will be their average speed, +s+
Let +d+ = the distance from Salt Lake City
+d%5B1%5D+ = the distance they have already traveled
The equation looks like:
+d+=+s%2At+%2B+d%5B1%5D+
Set +t+=+0+ to find +d%5B1%5D+
+d%5B1%5D+=+507++
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Between 8 hrs and 4 hrs of driving, they have been
driving 4 hrs and have traveled +507+-+267+=+240+ mi
+s+=+240%2F4+
+s+=+60+
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I come up with:
+d+=+-60t+%2B+507+
--------------------
I made the slope negative because +d+ has to get smaller
as +t+ increases
Here's a plot:
+graph%28+400%2C+400%2C+-1%2C+10%2C+-50%2C+600%2C+-60x+%2B+507+%29+
It looks like they get to Salt Lake City about 8.5 hrs since they
were 507 miles away ( at +t=0+ )
Hope this helps