Question

Professor Mahajani and Vishwanathan teach sociology. Their students recently took their final exams, and the professor are preparing to grade them. If If Professor Mahajani grades all the exams, he would take $50\%$ more time than Professor vishwanathan would take to grade all the exams. They estimate that it will take them $40$ hours to grade all the exams if they grade together. Which of the following equations best represents the situation described?

• A. $x+\frac{3}{2}x=40$
• B. $\frac{2}{x}+\frac{3}{x}=\frac{1}{20}$
• C. $\frac{1}{x}+\frac{50}{x}=\frac{1}{40}$
• D. $\frac{2}{x}+\frac{3}{x}=\frac{1}{40}$

Answer 1

Answer: (B)

$\frac{2}{x}+\frac{3}{x}=\frac{1}{20}$

Time by Professor Vishwanathan $=\frac{1}{x}$

Work by Professor Vishwanathan $=x$

Time by Professor Mahajani $=\frac{1}{x}+0.5$ of $\frac{1}{x}=\frac{1.5}{x}$

Total Time $=\frac{1}{40}$ (Expressed as work)

$\frac{1}{x}+\frac{1.5}{x}=\frac{1}{40}$

$\frac{3}{x}+\frac{2}{x}=\frac{1}{20}$