Question 993340
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=(7+- sqrt(65))/2)}}}
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