Terry has completed 15 homework problems and Suzanne has completed nine Terry is completing 10 problems for hour and Suzanne is completing 12 per hour after how many hours with Terry and Suzanne have completed the same number problems
After one hour, Terry will have completed 10 problems and Suzanne will have completed 12 problems.
After two hours, Terry will have completed 20 problems and Suzanne will have completed 24 problems.
After three hours, Terry will have completed 30 problems and Suzanne will have completed 36 problems.
After four hours, Terry will have completed 40 problems and Suzanne will have completed 48 problems.
After five hours, Terry will have completed 50 problems and Suzanne will have completed 60 problems.
Therefore, after five hours Terry and Suzanne will have completed the same number of problems.
To find out how many hours it will take for Terry and Suzanne to complete the same number of problems, we need to compare their total number of completed problems.
Terry completes 10 problems per hour, so after h hours, he will have completed 10h problems.
Suzanne completes 12 problems per hour, so after h hours, she will have completed 12h problems.
Given that Terry has completed 15 problems and Suzanne has completed 9, we can set up the following equation:
10h = 15
12h = 9
First, let's solve for Terry:
10h = 15
Divide both sides by 10:
h = 15/10
h = 1.5 hours
Now, let's solve for Suzanne:
12h = 9
Divide both sides by 12:
h = 9/12
h = 0.75 hours
Since h cannot be a fraction of an hour, we need to find a common whole number multiple of 1.5 and 0.75 hours.
The least common multiple (LCM) of 1.5 and 0.75 is 3 hours.
Therefore, Terry and Suzanne will have completed the same number of problems after 3 hours.