Answer :
Final answer:
They will have studied the same number of hours after 4 weeks. Maria studies 3 hours per week while Curtis studies 2 hours per week, with Curtis starting 4 hours ahead. After 4 weeks, Maria will have caught up, totaling 12 hours each.Thus option D is correct.
Explanation:
To solve this problem, we'll create a system of equations representing the hours studied by Maria and Curtis over time. Let ( M ) represent the total hours Maria has studied, and ( C ) represent the total hours Curtis has studied. We know that Maria studies German for 3 hours per week, and Curtis studies French for 2 hours per week. Curtis starts with 4 hours of study before Maria begins.
So, the equations representing their total hours studied over time are:
1.( M = 3w ) (Maria's study hours where ( w ) is the number of weeks)
2. ( C = 2(w - 4) ) (Curtis's study hours, adjusted for the 4 hours he already studied before Maria began)
To find when they've studied the same number of hours, we'll set these equations equal to each other:
( 3w = 2(w - 4) )
Now, solve for ( w ):
( 3w = 2w - 8 )
( w = 8 )
So, they will have studied the same number of hours after 8 weeks, but we need to account for the 4 hours Curtis studied before Maria began. Thus, the answer is ( 8 - 4 = 4 ) weeks. Therefore, the correct answer is option B) 4 weeks.
Thus option D is correct.