SOLUTION: 1) Sara set off on a bicycle trip at 6:30 am at an average rate of 24miles per hour. Her friend Jayne promised to bring her some lunch and she set off by motorcycle 2 hous after S

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: 1) Sara set off on a bicycle trip at 6:30 am at an average rate of 24miles per hour. Her friend Jayne promised to bring her some lunch and she set off by motorcycle 2 hous after S      Log On


   

Question 1085594: 1) Sara set off on a bicycle trip at 6:30 am at an average rate of 24miles per hour. Her friend Jayne promised to bring her some lunch and she set off by motorcycle 2 hous after Sara left, driving an average of 40 miles per hour. At what time did Jayne catch up with Sara?
2) Becky would like to have at least $100,000 saved for her daughter's college education. If she invests $25,000 in an education account paying 6/25% interest compounded quarterly, will she reach her goal in 16 years?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
What was Sarah's head start in miles?
+d+=+r%2At+
+d%5B1%5D+=+24%2A2+
+d%5B1%5D+=+48+ mi
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Start a stopwatch when Jane leaves and stop it
when she catches up with Sarah
( note that it is 8:30 AM when Jane leaves
Let +t+ = the time on the stopwatch in hours
Let +d+ = the distance in miles that Jane
travels until she ctches up with Sarah
-----------------------------------------------
Jane's equation:
(1) +d+=+40t+
Sarah's equation:
(2) +d+-+48+=+24t+
-------------------------
Plug (1) into (2)
(2) +40t+-+48+=+24t+
(2) +16t+=+48+
(2) +t+=+3+
--------------------
8:30 plus 3 hrs is 11:30 when
Jane catches up with Sarah
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check:
(1) +d+=+40t+
(1) +d+=+40%2A3+
(1) +d+=+120+ mi
and
(2) +d+-+48+=+24t+
(2) +d+-+48+=+24%2A3+
(2) +d+=+48+%2B+72+
(2) +d+=+120+ mi
OK
Note:
If you send a thank you note for this one, I
will answer the part 2 of your questions