SOLUTION: A teacher and his assistant can grade all student's exams in 4 hours. When the assistant does the grading by himself, it takes him an hour longer than it takes the teacher alone to

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A teacher and his assistant can grade all student's exams in 4 hours. When the assistant does the grading by himself, it takes him an hour longer than it takes the teacher alone to      Log On


   

Question 993340: A teacher and his assistant can grade all student's exams in 4 hours. When the assistant does the grading by himself, it takes him an hour longer than it takes the teacher alone to do the grading. Find how many hours it takes the teacher to do the grading by himself.
Type your numerical answer rounded to one decimal
Found 2 solutions by anand429, Leesoski:
Answer by anand429(138) About Me  (Show Source):
You can put this solution on YOUR website!
Let teacher can grade t students per hour and assistant can grade s students per hour
In 4 hours, no. of students graded = 4t + 4s
In 5 hours assistant can grade alone
so no. of students as per him = 5s
so, 4t + 4s = 5s
=> 4t = s
So time taken by teacher alone= (4t + 4s)/t
= (4t + 16t)/t
=20t/t
=20 hours.

Answer by Leesoski(1) About Me  (Show Source):
You can put this solution on YOUR website!
1/t + 1/(t+1) = 1/4
4(x+1) + 4x = x(x+1)
4x+4+4x = x^2 + x
8x + 4 = x^2 + x
0=x^2 - 7x -4
Solve with quadratic function:
x=%287%2B-+sqrt%2865%29%29%2F2%29
X=7+8.1/2
X=7.5 (rounded to one decimal place)
The time it takes the teacher alone to grade the tests is 7.5 hrs
We check the answer by plugging into the original equation:
1/7.5 + 1/8.5 = 1/4
7.5/64 + 8.5/64 = 16/64
16/64 = 1/4