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.
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.
it takes Gary two hours to catch up to Greg at the finish
because Gary goes 12 miles/hour, Greg finished 24 miles ahead of Gary
every hour, Greg travels 4 miles more than Gary
... so it took Greg 6 hours to get a 24 mile lead and finish the race
Greg goes 16 miles/hour, so in 6 hours he goes 96 miles
To solve this problem without using the time equation, you can use a simple method called the "Distance = Speed x Time" approach. Let's break it down for a 5th grader to understand.
We know that Greg and Gary started the race at the same time and place. The only difference is their speeds. Greg travels at 16 miles/hour, while Gary travels at 12 miles/hour.
Now, since Greg finished the race 2 hours ahead of Gary, it means that Greg has been biking longer than Gary. Let's denote the time Greg traveled as "t hours." Since Gary finished 2 hours later, he traveled for "t - 2" hours.
Now, let's calculate the distance traveled by each person. Remember, Distance = Speed x Time.
For Greg:
Distance Greg traveled = Speed Greg x Time Greg
Distance Greg traveled = 16 miles/hour x t hours
For Gary:
Distance Gary traveled = Speed Gary x Time Gary
Distance Gary traveled = 12 miles/hour x (t - 2) hours
Now, according to the problem, Greg traveled the entire race distance 2 hours faster than Gary. So we can say:
Distance Greg traveled = Distance Gary traveled
Using the equations we set up earlier:
16t = 12(t - 2)
Simplifying the equation:
16t = 12t - 24
Bringing all the "t" terms to one side of the equation:
16t - 12t = -24
Simplifying further:
4t = -24
Now, we need to solve for "t". We can divide both sides of the equation by 4:
t = -24/4
t = -6
Uh-oh, we obtained a negative value for "t", which doesn't make sense in this context. It means that something went wrong in our calculations.
In this case, it likely means that there is an error in the problem statement or in the information given. Please review the problem and make sure all the information is correct.
If you have any additional questions, feel free to ask!