SOLUTION: randy left town on his bicycle traveling at an average speed of 18 mph. Three hours later, his old brother jimmy went looking for him on his motorcycle traveling at an average of 5

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Question 835298: randy left town on his bicycle traveling at an average speed of 18 mph. Three hours later, his old brother jimmy went looking for him on his motorcycle traveling at an average of 54 mph. how long would it take jimmy to catch up on randy?

Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
Randy, slower, left earlier, traveled for more time, some t+3. Later, Jimmy on motorcycle, traveled t amount of time, at faster speed. You want to find t which both of them used, for the equal amount of distance (for "catchup").

highlight%2818%28t%2B3%29=54t%29, both members being that distance.
18t%2B54=54t
54=54t-18t
36t=54
t=54%2F36=27%2A2%2F%282%2A18%29=3%2A3%2A3%2A2%2F%282%2A2%2A3%2A3%29=3%2F2
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highlight%281%261%2F2%29 hours to catchup.