SOLUTION: Ivan and Kate live 42 miles apart. At 8 a.m., Ivan started biking towards Kate at a rate of 12 mph. Kate left to meet Ivan at 9:30 a.m., but biked at a rate of 18 mph. At what time

Algebra ->  Equations -> SOLUTION: Ivan and Kate live 42 miles apart. At 8 a.m., Ivan started biking towards Kate at a rate of 12 mph. Kate left to meet Ivan at 9:30 a.m., but biked at a rate of 18 mph. At what time      Log On


   

Question 1121343: Ivan and Kate live 42 miles apart. At 8 a.m., Ivan started biking towards Kate at a rate of 12 mph. Kate left to meet Ivan at 9:30 a.m., but biked at a rate of 18 mph. At what time did they meet? Please use as many steps as possible, so I can understand
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
Answer by ikleyn(52814) About Me  (Show Source):
You can put this solution on YOUR website!
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Ivan started first, and from 8 am till 9:30 am he moved toward Kate 12 mph * 1.5 hours = 18 miles.


So, at 9:30 am the distance between them is  42 - 18 = 24 miles.


Starting from 9:30 am they BOTH move toward each other.  Their relative speed is 12 + 18 = 30 miles per hour.


So, they will cover the distance of 24 miles between them in  24%2F30 = 4%2F5 hours, which is 48 minutes.


So, they will meet each other 48 minutes after 9:30 am,  which is  10:18 am.

Solved.


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For introductory lessons on Travel and Distance for beginners see 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.