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Greg and Gary start a bicycle race at the same place and time.Greg travels at a constant speed of 16 miles/hour and Gary at a constant speed of 12 miles/hour. Greg finishes the race 2 hours ahead of Gary. How many miles did Greg travel in the race?

Please help me with a simple solution that a 5th grader would understand.

The method has to be without having to use the time equation,he has not studied time = dist/speed

Thank you in advance.

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Perhaps you could make an argument about how many miles Greg needs to travel in order to get 1 hour ahead of Gary. This will occur when Greg has traveled 12 miles further than Gary. You could make a table showing how far they have traveled at each hour. After 3 hours, Greg should be 12 miles ahead of Gary. Thus, after 6 hours, Greg will be 24 miles ahead of Gary and Gary will need to continue racing for 2 hours to reach Greg's current location. To complete the problem, add up the distances.

I tutor an advanced student around the same level. The book we use has a lot of tables.

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  • $\begingroup$ Another idea for a table or graphic - make a timeline showing how far each has gone after each hour. Then find the distance at which they are 2 hours apart. $\endgroup$ – Browning Feb 18 '18 at 22:46
  • $\begingroup$ Thank you Bryan. I think making a table may be the simplest method to teach my son.This really helps.Once he gets it then I can move on to quicker methods. May I know which book do you use for tutoring your advanced student? $\endgroup$ – Pearl Feb 19 '18 at 21:11
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In the first hour Greg does $16$ miles, while Gary needs $20$ minutes more to reach that point. At the $2$ hours mark of Greg his friend is already $40$ minutes late, and so on. It follows that after $6$ hours Greg is exactly $2$ hours ahead of Gary. This means that the destination is $96$ miles away from the starting point.

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