Question

Professor J can grade an entire section of essays in 3 hours. His teaching assistant, M, can grade the same amount of essays in 5 hours. How long would it take them to grade the essays if they work together?
(15points) plz help!

Answer 1

Answer:

The time it takes them to grade the essays if they work together is 1.857 hours

Step-by-step explanation:

• Let t1 is time taken by Professor J = 3 hours
• Let t2 is time taken by the assistant = 5 hours
• Let tb is the time taken by both

The formula for “Work” Problems that involve two persons is

$\frac{1}{t1} + \frac{1}{t2} =\frac{1}{tb}$

<=> $\frac{1}{3} + \frac{1}{5} =\frac{1}{tb}$

<=> $\frac{1}{tb} = \frac{8}{15}$

<=> tb = $\frac{15}{8} = 1.875 hours$

The time it takes them to grade the essays if they work together is 1.857 hours