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.
On
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.
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.